Journal articles: 'Unbiased Estimation of Estimator Variance'

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Thanoon, Shaymaa Riyadh. "A comparison between Bayes estimation and the estimation of the minimal unbiased quadratic Standard of the bi-division variance analysis model in the presence of interaction." Tikrit Journal of Pure Science 25, no. 2 (March 17, 2020): 116. http://dx.doi.org/10.25130/j.v25i2.966.

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In this study, the variance compounds parameters of the mixed bi-division variance analysis sample are estimated. This estimation is obtained, by Bayes quadratic unbiased estimator. The second way to estimate variance compounds parameters of a suggested tow-way analysis of variance mixed model with interaction. estimation is done out by the approach called (MINQUÉ). The estimation approach is conducted on true obtained from departments at the college of agriculture/university of Mosul. These data represent the development of growing various kinds of tomato so that the development represents three factors: the first is tomato kind, this is the first factor (H) and the factor of natural fertilizer rate, and this is the second factor (M), and the interaction between the two factors (HM). A random sample is taken from these data in order to get the random linear sample. The elementary values estimated by Bayes unbiased estimator are very much close to those estimated by variance analysis style when compared with the estimated values of the variance estimation parameters done by minimum standard quadratic unbiased estimation. The elementary values represent random linear sample parameters used to estimate minimum quadratic unbiased standard. The elementary values of the estimations are also obtained via analyzing bi-division variance, then these estimations are employed in estimating minimum quadratic unbiased standard. the estimation results by Bayes approach are very similar to those done by variance analysis http://dx.doi.org/10.25130/tjps.25.2020.038

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Aladeitan, BENEDICTA, Adewale F. Lukman, Esther Davids, Ebele H. Oranye, and Golam B. M. Kibria. "Unbiased K-L estimator for the linear regression model." F1000Research 10 (August 19, 2021): 832. http://dx.doi.org/10.12688/f1000research.54990.1.

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Background: In the linear regression model, the ordinary least square (OLS) estimator performance drops when multicollinearity is present. According to the Gauss-Markov theorem, the estimator remains unbiased when there is multicollinearity, but the variance of its regression estimates become inflated. Estimators such as the ridge regression estimator and the K-L estimators were adopted as substitutes to the OLS estimator to overcome the problem of multicollinearity in the linear regression model. However, the estimators are biased, though they possess a smaller mean squared error when compared to the OLS estimator. Methods: In this study, we developed a new unbiased estimator using the K-L estimator and compared its performance with some existing estimators theoretically, simulation wise and by adopting real-life data. Results: Theoretically, the estimator even though unbiased also possesses a minimum variance when compared with other estimators. Results from simulation and real-life study showed that the new estimator produced smaller mean square error (MSE) and had the smallest mean square prediction error (MSPE). This further strengthened the findings of the theoretical comparison using both the MSE and the MSPE as criterion. Conclusions: By simulation and using a real-life application that focuses on modelling, the high heating values of proximate analysis was conducted to support the theoretical findings. This new method of estimation is recommended for parameter estimation with and without multicollinearity in a linear regression model.

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Hamza Raheem, Sairan. "Comparison Among Three Estimation Methods to Estimate Cascade Reliability Model (2+1) Based On Inverted Exponential Distribution." Ibn AL- Haitham Journal For Pure and Applied Sciences 33, no. 4 (October 20, 2020): 82. http://dx.doi.org/10.30526/33.4.2512.

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In this paper, we are mainly concerned with estimating cascade reliability model (2+1) based on inverted exponential distribution and comparing among the estimation methods that are used . The maximum likelihood estimator and uniformly minimum variance unbiased estimators are used to get of the strengths and the stress ;k=1,2,3 respectively then, by using the unbiased estimators, we propose Preliminary test single stage shrinkage (PTSSS) estimator when a prior knowledge is available for the scale parameter as initial value due past experiences . The Mean Squared Error [MSE] for the proposed estimator is derived to compare among the methods. Numerical results about conduct of the considered estimator are discussed including the study of mentioned expressions. The numerical results are exhibited and put it in tables.

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Vincent, Odhiambo, Hellen Waititu, and Nyakundi Omwando Cornelious. "Nonparametric Estimation of Error Variance under Simple Random Sampling without Replacement." International Journal of Mathematics And Computer Research 10, no. 10 (October 21, 2022): 2925–33. http://dx.doi.org/10.47191/ijmcr/v10i10.02.

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This study adopts a nonparametric approach in the estimation of a finite population error variance in the setting where the variance is a constant (homoscedastic) using a model-based technique under simple random sampling without replacement (SRSWOR). A mean square analysis of the estimator has been conducted, including the asymptotic behaviour of the estimator and the results show that the asymptotic distribution in a homoscedastic setting is asymptotically unbiased and consistent. The performance of the developed estimator is compared to that of other existing estimators using real data. R statistical software was utilized to analyze data and numerical results presented graphically for selected models.

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Rytgaard, Mette. "Estimation in the Pareto Distribution." ASTIN Bulletin 20, no. 2 (November 1990): 201–16. http://dx.doi.org/10.2143/ast.20.2.2005443.

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AbstractIn the present paper, different estimators of the Pareto parameter α will be proposed and compared to each others.First traditional estimators of α as the maximum likelihood estimator and the moment estimator will be deduced and their statistical properties will be analyzed. It is shown that the maximum likelihood estimator is biased but it can easily be modified to an minimum-variance unbiased estimator of a. But still the coefficient of variance of this estimator is very large.For similar portfolios containing same types of risks we will expect the estimated α-values to be at the same level. Therefore, credibility theory is used to obtain an alternative estimator of α which will be more stable and less sensitive to random fluctuations in the observed losses.Finally, an estimator of the risk premium for an unlimited excess of loss cover will be proposed. It is shown that this estimator is a minimum-variance unbiased estimator of the risk premium. This estimator of the risk premium will be compared to the more traditional methods of calculating the risk premium.

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Pisarenko, V. F., A. A. Lyubushin, V. B. Lysenko, and T. V. Golubeva. "Statistical estimation of seismic hazard parameters: Maximum possible magnitude and related parameters." Bulletin of the Seismological Society of America 86, no. 3 (June 1, 1996): 691–700. http://dx.doi.org/10.1785/bssa0860030691.

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Abstract The problem of statistical estimation of earthquake hazard parameters is considered. The emphasis is on estimation of the maximum regional magnitude, Mmax, and the maximum magnitude, Mmax(T), in a future time interval T and quantiles of its distribution. Two estimators are suggested: an unbiased estimator with the lowest possible variance and a Bayesian estimator. As an illustration, these methods are applied for the estimation of Mmax and related parameters in California and Italy.

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Villanueva, Beatriz, and Javier Moro. "Variance and efficiency of the combined estimator in incomplete block designs of use in forest genetics: a numerical study." Canadian Journal of Forest Research 31, no. 1 (January 1, 2001): 71–77. http://dx.doi.org/10.1139/x00-138.

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The efficiency of combined interblock-intrablock and intrablock analysis for the estimation of treatment contrasts in alpha designs is compared using Monte-Carlo simulation. The combined estimator considers treatments and replications as fixed effects and blocks as random effects, whereas the intrablock estimator considers treatments, replications, and blocks as fixed effects. The variances of the estimators are used as the criterion for comparison. The combined estimator yields more accurate estimates than the intrablock estimator when the ratio of the block to the error variance is small, especially for designs with the fewest degrees of freedom. The accuracy of both estimators is similar when the ratio of variances is large. The variance of the combined estimator is very close to that of the best linear unbiased estimator except for designs with small number of replicates and families or provenances. Approximations commonly used for the variance of the combined estimator when variances of the random effects are unknown are studied. The downward or negative bias in the estimates of the variance given by the standard approximation used in statistical packages is largest under the conditions in which the combined estimator is more efficient than the intrablock estimator. Estimates of the relative efficiency of combined estimators have an upward bias that can exceed 10% of the true value in small- and middle-sized designs with two or three replicates. In designs with four or more replicates, often used in forest genetics, the bias is negligible.

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Hahn, Ute, and Dietrich Stoyan. "Unbiased stereological estimation of the surface area of gradient surface processes." Advances in Applied Probability 30, no. 4 (December 1998): 904–20. http://dx.doi.org/10.1239/aap/1035228199.

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An unbiased stereological estimator for surface area density is derived for gradient surface processes which form a particular class of non-stationary spatial surface processes. Vertical planar sections are used for the estimation. The variance of the estimator is studied and found to be infinite for certain types of surface processes. A modification of the estimator is presented which exhibits finite variance.

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Hahn, Ute, and Dietrich Stoyan. "Unbiased stereological estimation of the surface area of gradient surface processes." Advances in Applied Probability 30, no. 04 (December 1998): 904–20. http://dx.doi.org/10.1017/s0001867800008715.

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An unbiased stereological estimator for surface area density is derived for gradient surface processes which form a particular class of non-stationary spatial surface processes. Vertical planar sections are used for the estimation. The variance of the estimator is studied and found to be infinite for certain types of surface processes. A modification of the estimator is presented which exhibits finite variance.

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Ng, Set Foong, Pei Eng Ch’ng, Yee Ming Chew, and Kok Shien Ng. "Applying the Method of Lagrange Multipliers to Derive an Estimator for Unsampled Soil Properties." Scientific Research Journal 11, no. 1 (June 1, 2014): 15. http://dx.doi.org/10.24191/srj.v11i1.5416.

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Soil properties are very crucial for civil engineers to differentiate one type of soil from another and to predict its mechanical behavior. However, it is not practical to measure soil properties at all the locations at a site. In this paper, an estimator is derived to estimate the unknown values for soil properties from locations where soil samples were not collected. The estimator is obtained by combining the concept of the ‘Inverse Distance Method’ into the technique of ‘Kriging’. The method of Lagrange Multipliers is applied in this paper. It is shown that the estimator derived in this paper is an unbiased estimator. The partiality of the estimator with respect to the true value is zero. Hence, the estimated value will be equal to the true value of the soil property. It is also shown that the variance between the estimator and the soil property is minimised. Hence, the distribution of this unbiased estimator with minimum variance spreads the least from the true value. With this characteristic of minimum variance unbiased estimator, a high accuracy estimation of soil property could be obtained.

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Ng, Set Foong, Pei Eng Ch’ng, Yee Ming Chew, and Kok Shien Ng. "Applying the Method of Lagrange Multipliers to Derive an Estimator for Unsampled Soil Properties." Scientific Research Journal 11, no. 1 (June 1, 2014): 15. http://dx.doi.org/10.24191/srj.v11i1.9398.

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Soil properties are very crucial for civil engineers to differentiate one type of soil from another and to predict its mechanical behavior. However, it is not practical to measure soil properties at all the locations at a site. In this paper, an estimator is derived to estimate the unknown values for soil properties from locations where soil samples were not collected. The estimator is obtained by combining the concept of the ‘Inverse Distance Method’ into the technique of ‘Kriging’. The method of Lagrange Multipliers is applied in this paper. It is shown that the estimator derived in this paper is an unbiased estimator. The partiality of the estimator with respect to the true value is zero. Hence, the estimated value will be equal to the true value of the soil property. It is also shown that the variance between the estimator and the soil property is minimised. Hence, the distribution of this unbiased estimator with minimum variance spreads the least from the true value. With this characteristic of minimum variance unbiased estimator, a high accuracy estimation of soil property could be obtained.

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Sohail, Muhammad Umair, Nursel Koyuncu, and Muhammad Areeb Iqbal Sethi. "Almost Unbiased Estimation of Coefficient of Dispersion from Incomplete Data." STATISTICS, COMPUTING AND INTERDISCIPLINARY RESEARCH 3, no. 2 (December 31, 2021): 143–54. http://dx.doi.org/10.52700/scir.v3i2.110.

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This article develops an almost unbiased estimation of coefficient of dispersion by the productive use of coefficient of dispersion of the auxiliary variable in two phase sampling. Expressions for variances of the proposed estimators are obtained up to first order of approximation. The relative comparision of proposed unbiased ratio estimator are compared with navie estimator by using simulated data sets. Thus, we conclude that the suggested imputation methodology is more efficient than traditional estimator.

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Sohail, Muhammad Umair, Nursel Koyuncu, and Muhammad Areeb Iqbal Sethi. "Almost Unbiased Estimation of Coefficient of Dispression from Imputed Data." STATISTICS, COMPUTING AND INTERDISCIPLINARY RESEARCH 3, no. 2 (December 31, 2021): 143–54. http://dx.doi.org/10.52700/scir.v3i2.55.

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This article develops an almost unbiased estimation of coefficient of dispersion by the productive use of coefficient of dispersion of the auxiliary variable in two phase sampling. Expressions for variances of the proposed estimators are obtained up to first order of approximation. The relative efficiencies of proposed unbiased ratio estimator are compared with navie estimator by using simulated data sets. Thus, we conclude that the proposed imputation procedure is more efficient than traditional estimator.

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Sohail, Muhammad Umair, Nursel Koyuncu, and Muhammad Areeb Iqbal Sethi. "Almost Unbiased Estimation of Coefficient of Dispression from Imputed Data." STATISTICS, COMPUTING AND INTERDISCIPLINARY RESEARCH 3, no. 2 (December 31, 2021): 143–54. http://dx.doi.org/10.52700/scir.v3i2.55.

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This article develops an almost unbiased estimation of coefficient of dispersion by the productive use of coefficient of dispersion of the auxiliary variable in two phase sampling. Expressions for variances of the proposed estimators are obtained up to first order of approximation. The relative efficiencies of proposed unbiased ratio estimator are compared with navie estimator by using simulated data sets. Thus, we conclude that the proposed imputation procedure is more efficient than traditional estimator.

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Jernot, Jean-Paul, Patricia Jouannot, and Christian Lantuéjoul. "UNBIASED ESTIMATORS OF SPECIFIC CONNECTIVITY." Image Analysis & Stereology 26, no. 3 (May 3, 2011): 129. http://dx.doi.org/10.5566/ias.v26.p129-136.

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This paper deals with the estimation of the specific connectivity of a stationary random set in IRd. It turns out that the "natural" estimator is only asymptotically unbiased. The example of a boolean model of hypercubes illustrates the amplitude of the bias produced when the measurement field is relatively small with respect to the range of the random set. For that reason unbiased estimators are desired. Such an estimator can be found in the literature in the case where the measurement field is a right parallelotope. In this paper, this estimator is extended to apply to measurement fields of various shapes, and to possess a smaller variance. Finally an example from quantitative metallography (specific connectivity of a population of sintered bronze particles) is given.

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Mehta, Nitu, and V. L. Mandowara. "Some Efficient Methods to Remove Bias in Ratio and Product Types Estimators in Ranked Set Sampling." International Journal of Bio-resource and Stress Management 13, no. 3 (March 31, 2022): 276–82. http://dx.doi.org/10.23910/1.2022.2771a.

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Ranked set sampling is one method to potentially increase precision and reduce costs by using quantitative or qualitative information to obtain a more representative sample. Use of auxiliary information has shown its significance in improvement of efficiency of estimators of unknown population parameters. Ratio estimator is used when auxiliary information in the form of population mean of auxiliary variable at estimation stage for the estimation of population parameters when study and auxiliary variable are positively correlated. In case of negative correlation between study variable and auxiliary variable, Product estimator is defined for the estimation of population mean. This paper proposed the problem of reducing the bias of the ratio and product estimators of the population mean in ranked set sampling (RSS). This paper suggested several type unbiased estimators of the finite population mean using information on known population parameters of the auxiliary variable in ranked set sampling. An important objective in any statistical estimation procedure is to obtain the estimators of parameters of interest with more precision. The Variance of the proposed unbiased ratio and product estimators are obtained up to first degree of approximation. Theoretically, it is shown that these suggested estimators are more efficient than the unbiased estimators in Simple random sampling. A numerical illustration is also carried out to demonstrate the merits of the proposed estimators using RSS over the usual estimators in SRS.

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Crittenden, R. N., G. L. Thomas, D. A. Marino, and R. E. Thorne. "A Weighted Duration-in-Beam Estimator for the Volume Sampled by a Quantitative Echo Sounder." Canadian Journal of Fisheries and Aquatic Sciences 45, no. 7 (July 1, 1988): 1249–56. http://dx.doi.org/10.1139/f88-147.

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Estimation of absolute fish density or abundance using the echo-count technique requires estimation of the volume sampled. The unknown parameter in the volume sampled is the sine of the half-angle of the effective conical beam. We derive the minimum variance, unbiased, linear estimator of this parameter. This estimator is based upon weighted regression through the origin and reduces to a computationally simple form. We use this estimate and its variance to estimate absolute density, absolute abundance, and their variances. We use a bootstrap procedure to contrast the performance of our method against that of a contemporary method, which is based upon the averages taken over range strata. Although both of these methods are unbiased, we show that our estimator has a standard deviation that is 23.5% smaller than that of the average-over-strata method.

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Chugg, Ben, Peter Henderson, Jacob Goldin, and Daniel E. Ho. "Entropy Regularization for Population Estimation." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 10 (June 26, 2023): 12198–204. http://dx.doi.org/10.1609/aaai.v37i10.26438.

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Entropy regularization is known to improve exploration in sequential decision-making problems. We show that this same mechanism can also lead to nearly unbiased and lower-variance estimates of the mean reward in the optimize-and-estimate structured bandit setting. Mean reward estimation (i.e., population estimation) tasks have recently been shown to be essential for public policy settings where legal constraints often require precise estimates of population metrics. We show that leveraging entropy and KL divergence can yield a better trade-off between reward and estimator variance than existing baselines, all while remaining nearly unbiased. These properties of entropy regularization illustrate an exciting potential for bringing together the optimal exploration and estimation literature.

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Kunes, Russell Z., Mingzhang Yin, Max Land, Doron Haviv, Dana Pe'er, and Simon Tavaré. "Gradient Estimation for Binary Latent Variables via Gradient Variance Clipping." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 7 (June 26, 2023): 8405–12. http://dx.doi.org/10.1609/aaai.v37i7.26013.

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Gradient estimation is often necessary for fitting generative models with discrete latent variables, in contexts such as reinforcement learning and variational autoencoder (VAE) training. The DisARM estimator achieves state of the art gradient variance for Bernoulli latent variable models in many contexts. However, DisARM and other estimators have potentially exploding variance near the boundary of the parameter space, where solutions tend to lie. To ameliorate this issue, we propose a new gradient estimator bitflip-1 that is lower variance at the boundaries of the parameter space. As bitflip-1 has complementary properties to existing estimators, we introduce an aggregated estimator, unbiased gradient variance clipping (UGC) that uses either a bitflip-1 or a DisARM gradient update for each coordinate. We theoretically prove that UGC has uniformly lower variance than DisARM. Empirically, we observe that UGC achieves the optimal value of the optimization objectives in toy experiments, discrete VAE training, and in a best subset selection problem.

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Mahdizadeh, M., and Ehsan Zamanzade. "Efficient reliability estimation in two-parameter exponential distributions." Filomat 32, no. 4 (2018): 1455–63. http://dx.doi.org/10.2298/fil1804455m.

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This article concerns reliability estimation in two-parameter exponential distributions setup with known scale parameters, and unknown location parameters. Based on the uniformly minimum variance unbiased estimator, we propose a new estimator and study its theoretical properties. Simulation results reveal that the suggested estimator could be highly efficient.

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Xiao, Min, Ting Chen, Kunpeng Huang, and Ruixing Ming. "Optimal Estimation for Power of Variance with Application to Gene-Set Testing." Journal of Systems Science and Information 8, no. 6 (December 1, 2020): 549–64. http://dx.doi.org/10.21078/jssi-2020-549-16.

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Abstract Detecting differential expression of genes in genom research (e.g., 2019-nCoV) is not uncommon, due to the cost only small sample is employed to estimate a large number of variances (or their inverse) of variables simultaneously. However, the commonly used approaches perform unreliable. Borrowing information across different variables or priori information of variables, shrinkage estimation approaches are proposed and some optimal shrinkage estimators are obtained in the sense of asymptotic. In this paper, we focus on the setting of small sample and a likelihood-unbiased estimator for power of variances is given under the assumption that the variances are chi-squared distribution. Simulation reports show that the likelihood-unbiased estimators for variances and their inverse perform very well. In addition, application comparison and real data analysis indicate that the proposed estimator also works well.

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Moothathu, T. S. K., and D. Christudas. "On Unbiased Estimation of GINI, PIESCH and MEHRAN Inequality Indices of Log-Laplace Distribution." Calcutta Statistical Association Bulletin 42, no. 3-4 (September 1992): 163–76. http://dx.doi.org/10.1177/0008068319920302.

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Here we develop the uniformly minimum variance unbiased (best) estimators and strongly consistent, asymptotically normal unbiased estimators ofGini,Piesch and Mehran inequality indices of Log-Laplace distribution. These estimators are in terms of the special functions 1 F9 and 1F1. The variance of each estimator and ths best estimator of each such variance are derived, which are in terms of certain special cases of Kempe de Feriet function, Appell function F2 and Humbert function ø2. Finally each estimator of this paper is shown to be strongly consistent.

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Mittal, Alisha, and Manoj Kumar. "GENERALISED EXPONENTIAL RATIO-TYPE ESTIMATOR FOR FINITE POPULATION VARIANCE UNDER RANDOM NON-RESPONSE." International Journal of Advanced Research 9, no. 01 (January 31, 2021): 589–96. http://dx.doi.org/10.21474/ijar01/12332.

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In this research paper an effort has been made for the estimation of population variance of the study variable by using information on certain known parameters of the auxiliary variable under non-response for scheme I and II given by Singh and Joarder (1998). Generalized exponential ratio-type estimator has been proposed and their properties have been studied under non response techniques and conditions were found when the family of proposed estimators identified by using different choices for (P, Q) performed better than the usual unbiased estimator. It was also observed that for different values of Î± âˆˆ (0.0, 1.0), the estimators and were found to be best under numerical illustration.

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Sjöberg, Lars. "On the Best Quadratic Minimum Bias Non-Negative Estimator of a Two-Variance Component Model." Journal of Geodetic Science 1, no. 3 (September 1, 2011): 280–85. http://dx.doi.org/10.2478/v10156-011-0006-y.

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On the Best Quadratic Minimum Bias Non-Negative Estimator of a Two-Variance Component ModelVariance components (VCs) in linear adjustment models are usually successfully computed by unbiased estimators. However, for many unbiased VC techniques estimated variance components might be negative, a result that cannot be tolerated by the user. This is, for example, the case with the simple additive VC model aσ2/1 + bσ2/2 with known coefficients a and b, where either of the unbiasedly estimated variance components σ2/1 + σ2/2 may frequently come out negative. This fact calls for so-called non-negative VC estimators. Here the Best Quadratic Minimum Bias Non-negative Estimator (BQMBNE) of a two-variance component model is derived. A special case with independent observations is explicitly presented.

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Ditlevsen, Susanne, and Petr Lansky. "Firing Variability Is Higher than Deduced from the Empirical Coefficient of Variation." Neural Computation 23, no. 8 (August 2011): 1944–66. http://dx.doi.org/10.1162/neco_a_00157.

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A convenient and often used summary measure to quantify the firing variability in neurons is the coefficient of variation (CV), defined as the standard deviation divided by the mean. It is therefore important to find an estimator that gives reliable results from experimental data, that is, the estimator should be unbiased and have low estimation variance. When the CV is evaluated in the standard way (empirical standard deviation of interspike intervals divided by their average), then the estimator is biased, underestimating the true CV, especially if the distribution of the interspike intervals is positively skewed. Moreover, the estimator has a large variance for commonly used distributions. The aim of this letter is to quantify the bias and propose alternative estimation methods. If the distribution is assumed known or can be determined from data, parametric estimators are proposed, which not only remove the bias but also decrease the estimation errors. If no distribution is assumed and the data are very positively skewed, we propose to correct the standard estimator. When defining the corrected estimator, we simply use that it is more stable to work on the log scale for positively skewed distributions. The estimators are evaluated through simulations and applied to experimental data from olfactory receptor neurons in rats.

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Lebrenz, Henning, and András Bárdossy. "Geostatistical interpolation by quantile kriging." Hydrology and Earth System Sciences 23, no. 3 (March 20, 2019): 1633–48. http://dx.doi.org/10.5194/hess-23-1633-2019.

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Abstract. The widely applied geostatistical interpolation methods of ordinary kriging (OK) or external drift kriging (EDK) interpolate the variable of interest to the unknown location, providing a linear estimator and an estimation variance as measure of uncertainty. The methods implicitly pose the assumption of Gaussianity on the observations, which is not given for many variables. The resulting “best linear and unbiased estimator” from the subsequent interpolation optimizes the mean error over many realizations for the entire spatial domain and, therefore, allows a systematic under-(over-)estimation of the variable in regions of relatively high (low) observations. In case of a variable with observed time series, the spatial marginal distributions are estimated separately for one time step after the other, and the errors from the interpolations might accumulate over time in regions of relatively extreme observations. Therefore, we propose the interpolation method of quantile kriging (QK) with a two-step procedure prior to interpolation: we firstly estimate distributions of the variable over time at the observation locations and then estimate the marginal distributions over space for every given time step. For this purpose, a distribution function is selected and fitted to the observed time series at every observation location, thus converting the variable into quantiles and defining parameters. At a given time step, the quantiles from all observation locations are then transformed into a Gaussian-distributed variable by a 2-fold quantile–quantile transformation with the beta- and normal-distribution function. The spatio-temporal description of the proposed method accommodates skewed marginal distributions and resolves the spatial non-stationarity of the original variable. The Gaussian-distributed variable and the distribution parameters are now interpolated by OK and EDK. At the unknown location, the resulting outcomes are reconverted back into the estimator and the estimation variance of the original variable. As a summary, QK newly incorporates information from the temporal axis for its spatial marginal distribution and subsequent interpolation and, therefore, could be interpreted as a space–time version of probability kriging. In this study, QK is applied for the variable of observed monthly precipitation from raingauges in South Africa. The estimators and estimation variances from the interpolation are compared to the respective outcomes from OK and EDK. The cross-validations show that QK improves the estimator and the estimation variance for most of the selected objective functions. QK further enables the reduction of the temporal bias at locations of extreme observations. The performance of QK, however, declines when many zero-value observations are present in the input data. It is further revealed that QK relates the magnitude of its estimator with the magnitude of the respective estimation variance as opposed to the traditional methods of OK and EDK, whose estimation variances do only depend on the spatial configuration of the observation locations and the model settings.

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Shanubhogue, Ashok, and N. R. Jain. "Minimum Variance Unbiased Estimation in the Gompertz Distribution under Progressive Type II Censored Data with Binomial Removals." ISRN Probability and Statistics 2013 (February 25, 2013): 1–7. http://dx.doi.org/10.1155/2013/237940.

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This paper deals with the problem of uniformly minimum variance unbiased estimation for the parameter of the Gompertz distribution based on progressively Type II censored data with binomial removals. We have obtained the uniformly minimum variance unbiased estimator (UMVUE) for powers of the shape parameter and its functions. The UMVUE of the variance of these estimators is also given. The UMVUE of (i) pdf, (ii) cdf, (iii) reliability function, and (iv) hazard function of the Gompertz distribution is derived. Further, an exact % confidence interval for the th quantile is obtained. The UMVUE of pdf is utilized to obtain the UMVUE of . An illustrative numerical example is presented.

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Haakana, Helena, Juha Heikkinen, Matti Katila, and Annika Kangas. "Precision of exogenous post-stratification in small-area estimation based on a continuous national forest inventory." Canadian Journal of Forest Research 50, no. 4 (April 2020): 359–70. http://dx.doi.org/10.1139/cjfr-2019-0139.

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National forest inventories (NFIs) are designed to provide accurate information on forest resources at the national and regional levels, but there is also a demand for such information at smaller spatial scales. Auxiliary data such as satellite imagery have been used to facilitate small-area estimation. The commonly used method, k-nearest neighbour (k-NN), provides a model-based estimator for small areas, but a design-unbiased estimator for the mean square error is not available. Post-stratification (PS) is an alternative approach to using auxiliary information that allows for design-based variance estimation. In a case study using real inventory data of the Finnish NFI, we applied this method to the municipality level to explore the lower limit to the area for which the key forest parameters, forest area and growing stock volumes, can be estimated with sufficient precision. For PS, we employed exogenous forest resources maps based on the previous NFI round. In the municipalities of the two study provinces, the relative standard errors of total volume estimates ranged from 2.3% to 26.9%. They were smaller than 10% for municipalities with an area of 390 km2 or larger, corresponding to approximately 100 or more sample plots on forestland. We also demonstrated the usefulness of design-unbiased variance estimation in showing discrepancies between design-based PS and model-based k-NN estimates.

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Janáček, Jiří, and Lucie Kubínová. "VARIANCES OF LENGTH AND SURFACE AREA ESTIMATES BY SPATIAL GRIDS: PRELIMINARY STUDY." Image Analysis & Stereology 29, no. 1 (May 3, 2011): 45. http://dx.doi.org/10.5566/ias.v29.p45-52.

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Periodic spatial grids can be used for unbiased estimation of length and surface area of objects by counting or measuring intersections of the objects with the grids. The estimators are theoretically based on discrete approximation of well established integral geometric formulas. The variance of the estimates depends on properties of both the grid and the measured objects. Main results of the theory of variance of the isotropic uniform random (IUR) volume estimation by spatial grids, especially a formula relating the variance of the volume estimator with the object surface area and the grid constant, are recapitulated. To identify main features of length and surface area IUR estimates the variance due to rotation and simple asymptotic formulas for the residual variance of estimates of selected model objects is calculated. Surface area estimates by multiple grids of parallel lines in 3D and of the variance of length estimates by periodic grids of planes or spheres in ddimensional space are studied.

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Hönekopp, Johannes, and Audrey Helen Linden. "Heterogeneity estimates in a biased world." PLOS ONE 17, no. 2 (February 3, 2022): e0262809. http://dx.doi.org/10.1371/journal.pone.0262809.

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Meta-analyses typically quantify heterogeneity of results, thus providing information about the consistency of the investigated effect across studies. Numerous heterogeneity estimators have been devised. Past evaluations of their performance typically presumed lack of bias in the set of studies being meta-analysed, which is often unrealistic. The present study used computer simulations to evaluate five heterogeneity estimators under a range of research conditions broadly representative of meta-analyses in psychology, with the aim to assess the impact of biases in sets of primary studies on estimates of both mean effect size and heterogeneity in meta-analyses of continuous outcome measures. To this end, six orthogonal design factors were manipulated: Strength of publication bias; 1-tailed vs. 2-tailed publication bias; prevalence of p-hacking; true heterogeneity of the effect studied; true average size of the studied effect; and number of studies per meta-analysis. Our results showed that biases in sets of primary studies caused much greater problems for the estimation of effect size than for the estimation of heterogeneity. For the latter, estimation bias remained small or moderate under most circumstances. Effect size estimations remained virtually unaffected by the choice of heterogeneity estimator. For heterogeneity estimates, however, relevant differences emerged. For unbiased primary studies, the REML estimator and (to a lesser extent) the Paule-Mandel performed well in terms of bias and variance. In biased sets of primary studies however, the Paule-Mandel estimator performed poorly, whereas the DerSimonian-Laird estimator and (to a slightly lesser extent) the REML estimator performed well. The complexity of results notwithstanding, we suggest that the REML estimator remains a good choice for meta-analyses of continuous outcome measures across varied circumstances.

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van Opheusden, Bas, Luigi Acerbi, and Wei Ji Ma. "Unbiased and efficient log-likelihood estimation with inverse binomial sampling." PLOS Computational Biology 16, no. 12 (December 23, 2020): e1008483. http://dx.doi.org/10.1371/journal.pcbi.1008483.

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The fate of scientific hypotheses often relies on the ability of a computational model to explain the data, quantified in modern statistical approaches by the likelihood function. The log-likelihood is the key element for parameter estimation and model evaluation. However, the log-likelihood of complex models in fields such as computational biology and neuroscience is often intractable to compute analytically or numerically. In those cases, researchers can often only estimate the log-likelihood by comparing observed data with synthetic observations generated by model simulations. Standard techniques to approximate the likelihood via simulation either use summary statistics of the data or are at risk of producing substantial biases in the estimate. Here, we explore another method, inverse binomial sampling (IBS), which can estimate the log-likelihood of an entire data set efficiently and without bias. For each observation, IBS draws samples from the simulator model until one matches the observation. The log-likelihood estimate is then a function of the number of samples drawn. The variance of this estimator is uniformly bounded, achieves the minimum variance for an unbiased estimator, and we can compute calibrated estimates of the variance. We provide theoretical arguments in favor of IBS and an empirical assessment of the method for maximum-likelihood estimation with simulation-based models. As case studies, we take three model-fitting problems of increasing complexity from computational and cognitive neuroscience. In all problems, IBS generally produces lower error in the estimated parameters and maximum log-likelihood values than alternative sampling methods with the same average number of samples. Our results demonstrate the potential of IBS as a practical, robust, and easy to implement method for log-likelihood evaluation when exact techniques are not available.

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32

Nayeban, S., A. Rezaei Roknabadi, and G. Mohtashami Borzadaran. "Lower bounds for the variance of unbiased estimators in generalized beta distribution of the second kind (GB2)." Studia Scientiarum Mathematicarum Hungarica 51, no. 2 (June 1, 2014): 172–85. http://dx.doi.org/10.1556/sscmath.51.2014.2.1274.

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In order to give an excellent description of income distributions, although a large number of functional forms have been proposed, but the four-parameter generalized beta model of the second kind (GB2), introduced by J. B. McDonald [18], is now widely acknowledged which is including many other models as special or limiting cases.One of the fundamentals of statistical inference is the estimation problem of a function of unknown parameter in a probability distribution and computing the variance of the estimator or approximating it by lower bounds.In this paper, we consider two famous lower bounds for the variance of any unbiased estimator, which are Bhattacharyya and Kshirsagar bounds. We obtain the general forms of the Bhattacharyya and Kshirsagar matrices in the GB2 distribution. In addition, we compare different Bhattacharyya and Kshirsagar bounds for the variance of any unbiased estimator of some parametric functions such as mode, mean, skewness and kurtosis in GB2 distribution and conclude that in each case, which bound is better to use. The results of this paper can be useful for researchers trying to find the accuracy of the estimators.

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33

Schreuder, H. T., Z. Ouyang, and M. Williams. "Point-Poisson, point-pps, and modified point-pps sampling: efficiency and variance estimation." Canadian Journal of Forest Research 22, no. 8 (August 1, 1992): 1071–78. http://dx.doi.org/10.1139/x92-142.

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Modified point-pps (probability proportional to size) sampling selects at least one sample tree per point and yields a fixed sample size. Point-Poisson sampling is as efficient as this modified procedure but less efficient than regular point-pps sampling in a simulation study estimating total volume using either the Horvitz–Thompson (ŶHT) or the weighted regression estimator (Ŷwr). Point-pps sampling is somewhat more efficient than point-Poisson sampling for all estimators except ŶHT, and point-Poisson sampling is always somewhat more efficient than modified point-pps sampling across.all estimators. For board foot volume the regression estimators are more efficient than ŶHT for all three procedures. Point-pps sampling is always most efficient, except for ŶHT, and point-Poisson sampling is always more efficient than the modified point-pps procedure. We recommend using Ŷgr (generalized regression estimator), Ŷwr, or ŶHT for total volume and Ŷgr for board foot volume. Three variance estimators estimate the variances of the regression estimates with small bias; we recommend the simple bootstrap variance estimator because it is simple to compute and does as well as its two main competitors. It does well for ŶHT, too, for all three procedures and should be used for ŶHT in point-Ppisson sampling in preference to the Grosenbaugh variance approximation. An unbiased variance estimator is given for ŶHT with the modified point-pps procedure, but the simple bootstrap variance is equally good.

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34

Raheem, Sairan Hamza, Bayda Atiya Kalaf, and Abbas Najim Salman. "Comparison of Some of Estimation methods of Stress-Strength Model: R = P(Y < X < Z)." Baghdad Science Journal 18, no. 2(Suppl.) (June 20, 2021): 1103. http://dx.doi.org/10.21123/bsj.2021.18.2(suppl.).1103.

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In this study, the stress-strength model R = P(Y < X < Z) is discussed as an important parts of reliability system by assuming that the random variables follow Invers Rayleigh Distribution. Some traditional estimation methods are used to estimate the parameters namely; Maximum Likelihood, Moment method, and Uniformly Minimum Variance Unbiased estimator and Shrinkage estimator using three types of shrinkage weight factors. As well as, Monte Carlo simulation are used to compare the estimation methods based on mean squared error criteria.

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35

Zhu, Jun, and Bruce S. Weir. "Mixed model approaches for diallel analysis based on a bio-model." Genetical Research 68, no. 3 (December 1996): 233–40. http://dx.doi.org/10.1017/s0016672300034200.

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SummaryA MINQUE(l) procedure, which is minimum norm quadratic unbiased estimation (MINQUE) method with 1 for all the prior values, is suggested for estimating variance and covariance components in a bio-model for diallel crosses. Unbiasedness and efficiency of estimation were compared for MINQUE(l), restricted maximum likelihood (REML) and MINQUE(θ) which has parameter values for the prior values. MINQUE(l) is almost as efficient as MINQUE(θ) for unbiased estimation of genetic variance and covariance components. The bio-model is efficient and robust for estimating variance and covariance components for maternal and paternal effects as well as for nuclear effects. A procedure of adjusted unbiased prediction (AUP) is proposed for predicting random genetic effects in the bio-model. The jack-knife procedure is suggested for estimation of sampling variances of estimated variance and covariance components and of predicted genetic effects. Worked examples are given for estimation of variance and covariance components and for prediction of genetic merits.

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36

Meyer, Luc, Dalil Ichalal, and Vincent Vigneron. "A new unbiased minimum variance observer for stochastic LTV systems with unknown inputs." IMA Journal of Mathematical Control and Information 37, no. 2 (March 20, 2019): 475–96. http://dx.doi.org/10.1093/imamci/dnz009.

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Abstract This paper is devoted to the state and input estimation of a linear time varying system in the presence of an unknown input (UI) in both state and measurement equations, and affected by Gaussian noises. The classical rank condition used in this kind of approach is relaxed in order to be able to be used in a wider range of systems. A state observer, that is an unbiased estimator with minimum error variance, is proposed. Then a UI observer is constructed, in order to be a best linear unbiased estimator, it follows a unique construction whether the direct feedthrough matrix is null or not. In a sense the proposed approach, generalizes and unifies the existing ones. Besides, a stability result is given for linear time invariant systems, which is a novelty for unbiased minimum variance observers relaxing the classical rank condition.

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37

Hansen, Bruce E. "A Modern Gauss–Markov Theorem." Econometrica 90, no. 3 (2022): 1283–94. http://dx.doi.org/10.3982/ecta19255.

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This paper presents finite‐sample efficiency bounds for the core econometric problem of estimation of linear regression coefficients. We show that the classical Gauss–Markov theorem can be restated omitting the unnatural restriction to linear estimators, without adding any extra conditions. Our results are lower bounds on the variances of unbiased estimators. These lower bounds correspond to the variances of the the least squares estimator and the generalized least squares estimator, depending on the assumption on the error covariances. These results show that we can drop the label “linear estimator” from the pedagogy of the Gauss–Markov theorem. Instead of referring to these estimators as BLUE, they can legitimately be called BUE (best unbiased estimators).

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38

Ginestet, Cedric E., Richard Emsley, and Sabine Landau. "Stein-like estimators for causal mediation analysis in randomized trials." Statistical Methods in Medical Research 29, no. 4 (June 7, 2019): 1129–48. http://dx.doi.org/10.1177/0962280219852388.

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Causal mediation analysis aims to estimate natural direct and natural indirect effects under clearly specified assumptions. Traditional mediation analysis based on Ordinary Least Squares assumes an absence of unmeasured causes to the putative mediator and outcome. When these assumptions cannot be justified, instrumental variable estimators can be used in order to produce an asymptotically unbiased estimator of the mediator-outcome link, commonly referred to as a Two-Stage Least Squares estimator. Such bias removal, however, comes at the cost of variance inflation. A Semi-Parametric Stein-Like estimator has been proposed in the literature that strikes a natural trade-off between the unbiasedness of the Two-Stage Least Squares procedure and the relatively small variance of the Ordinary Least Squares estimator. The Semi-Parametric Stein-Like estimator has the advantage of allowing for a direct estimation of its shrinkage parameter. In this paper, we demonstrate how this Stein-like estimator can be implemented in the context of the estimation of natural direct and natural indirect effects of treatments in randomized controlled trials. The performance of the competing methods is studied in a simulation study, in which both the strength of hidden confounding and the strength of the instruments are independently varied. These considerations are motivated by a trial in mental health, evaluating the impact of a primary care-based intervention to reduce depression in the elderly.

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39

Li, Zhengzheng, Yan Zhang, and Scott E. Giangrande. "Rainfall-Rate Estimation Using Gaussian Mixture Parameter Estimator: Training and Validation." Journal of Atmospheric and Oceanic Technology 29, no. 5 (May 1, 2012): 731–44. http://dx.doi.org/10.1175/jtech-d-11-00122.1.

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Abstract This study develops a Gaussian mixture rainfall-rate estimator (GMRE) for polarimetric radar-based rainfall-rate estimation, following a general framework based on the Gaussian mixture model and Bayes least squares estimation for weather radar–based parameter estimations. The advantages of GMRE are 1) it is a minimum variance unbiased estimator; 2) it is a general estimator applicable to different rain regimes in different regions; and 3) it is flexible and may incorporate/exclude different polarimetric radar variables as inputs. This paper also discusses training the GMRE and the sensitivity of performance to mixture number. A large radar and surface gauge observation dataset collected in central Oklahoma during the multiyear Joint Polarization Experiment (JPOLE) field campaign is used to evaluate the GMRE approach. Results indicate that the GMRE approach can outperform existing polarimetric rainfall techniques optimized for this JPOLE dataset in terms of bias and root-mean-square error.

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40

AL-Mouel, Abdulhussein Saber, and Jasim Mohammed Ali. "Best Quadratic unbiased Estimator for Variance Component of One-Way Repeated Measurement Model." JOURNAL OF ADVANCES IN MATHEMATICS 14, no. 1 (April 30, 2018): 7615–23. http://dx.doi.org/10.24297/jam.v14i1.7342.

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The studies of analysis of variance components is one of the important topics in mathematical statistics for this subject of wide application. In this paper given best quadratic unbiased estimator of variance components for balanced data for linear one-way repeated measurement model (RMM). We computed the quadratic unbiased estimator, which has minimum variance (best quadratic unbiased estimate (BQUE)) by using analysis of variance (ANOVA) method of estimating the variance components.

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41

Nayak, Tapan Kumar. "Estimating the Parameter of a Selected Population." Calcutta Statistical Association Bulletin 45, no. 1-2 (March 1995): 93–102. http://dx.doi.org/10.1177/0008068319950105.

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Suppose independent samples from k populations with unknown parameters are taken and one of the populations is selected based on tho data and a prespecified rule. The problem is to estimate the parameter of the selected population. The estimand, G, is a random quantity which depends on both the data and the unknown parameters. While standard estimation methods are inadequate for estimating G, they can be used to estimate the expected value of G. It is shown that the uniformly minimum variance unbiased estimator of E( G) is also the uniformly minimum mean squared error unbiased estimator of G, if the selection rule depends on the data only through a complete sufficient statistic. An approach based on conditional unbiasedness is also discussed.

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42

Crittenden, R. N., and G. L. Thomas. "A Conditional Generalized Least Squares Method for Estimating the Size of a Closed Population." Canadian Journal of Fisheries and Aquatic Sciences 46, no. 5 (May 1, 1989): 818–23. http://dx.doi.org/10.1139/f89-102.

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In the corrected Leslie–DeLury catch-per-unit-effort method, estimation of the corrected cumulative catches causes the underlying model to be an errors-in-covariates structural model with a nondiagonal dispersion matrix. This violates the assumptions of regression and causes the corrected Leslie–DeLury method to give biased estimates of the population size and its variance. We use generalized least squares and a controlled variables design to resolve these difficulties, obtain the minimum-variance unbiased linear estimator, and compute unbiased variance estimates. We apply our method to sockeye salmon fingerlings (Oncorhynchus nerka) netted in a hatchery pond. For these data, arranged according to the controlled variables design, the corrected Leslie–DeLury method underestimates the standard error of the population size by 41%.

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Korir, Betty C., and Josphat K. Kinyanjui. "Parametric Interval Estimation of the Geeta Distribution." International Journal of Statistics and Probability 8, no. 1 (November 19, 2018): 1. http://dx.doi.org/10.5539/ijsp.v8n1p1.

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It is well known that the sample mean is the estimator of a population mean in mathematical statistics from a given population of interest as a point estimator which assume a single number that is obtained by taking a random sample of a specified size from the entire population, depending on whether the population mean and variance is known or unknown. In the interval estimation, the sample mean is accompanied with a plus or a minus margin of an error that is assumed that the estimator is contained within the range of values with certain degree of confidence. This paper investigated and obtained the interval estimators of the unknown constants of Geeta distribution model through the construction of confidence interval using; the pivotal quantity method, the shortest-length confidence interval, unbiased confidence interval estimators, Bayesian confidence interval estimators and statistical method. Geeta distribution is a new discrete random variable distribution defined over all the positive integers, with two unknown parameters. The properties and characteristics of the Geeta distribution model were discussed and reviewed that is, the existence of the mean, variance, moment generating function and that the sum of all probabilities is unity. These are common properties of any given probability density function.

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Chaturvedi, Aditi, and Surinder Kumar. "Estimation procedures for reliability functions of Kumaraswamy-G Distributions based on Type II Censoring and the sampling scheme of Bartholomew." Statistics in Transition New Series 23, no. 1 (March 1, 2022): 129–52. http://dx.doi.org/10.2478/stattrans-2022-0008.

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Abstract In this paper, we consider Kumaraswamy-G distributions and derive a Uniformly Minimum Variance Unbiased Estimator (UMVUE) and a Maximum Likelihood Estimator (MLE) of the two measures of reliability, namely R(t) = P(X > t) and P = P(X > Y) under Type II censoring scheme and sampling scheme of Bartholomew (1963). We also develop interval estimates of the reliability measures. A comparative study of the different methods of point estimation has been conducted on the basis of simulation studies. An analysis of a real data set has been presented for illustration purposes.

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45

Angus, John E. "The Improved Estimation of σ in Quality Control, Revisited." Probability in the Engineering and Informational Sciences 11, no. 1 (January 1997): 37–42. http://dx.doi.org/10.1017/s0269964800004654.

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Recently, Derman and Ross (1995, An improved estimator of a in quality control, Probability in the Engineering and Informational Sciences 9: 411–415) derived an estimator of the standard deviation in the standard quality control model and showed that it had smaller mean squared error than the usual estimator. The new estimator was also shown to be consistent even when the underlying distribution deviates from normality, unlike the usual estimator. In this note, the mean squared error is further improved via shrinkage of the Derman-Ross estimator, and a consistent minimum variance unbiased estimator is presented. Finally, by making use of additional subgroup statistics, a minimum variance unbiased estimator is derived and further improved via shrinkage.

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Biradar, R. S., and H. P. Singh. "Predictive Estimation of Finite Population Variance." Calcutta Statistical Association Bulletin 48, no. 3-4 (September 1998): 229–36. http://dx.doi.org/10.1177/0008068319980310.

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Adopting predictive approach, estimators are proposed for population variance [Formula: see text] using different predictors for mean and variance of unobserved units in the population. Asymptotic expressions for bias and mean square error of these new estimators are obtained and compared with those of some known estimators of population variance. Predictive character of some known estimators is also examined . An empirical study demonstrated superiority over others of one of the proposed estimators, which uses regression estimators as predictors for mean and variance of unobserved units. Also, one of the other proposed estimators which does not utilize any auxiliary information has been found to be more efficient than the traditional unbiased estimator [Formula: see text].

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Cebrián, A. Arcos, and M. Rueda García. "Variance estimation using auxiliary information: An almost unbiased multivariate ratio estimator." Metrika 45, no. 1 (January 1997): 171–78. http://dx.doi.org/10.1007/bf02717100.

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48

Pospisil, Dean A., and Wyeth Bair. "The unbiased estimation of the fraction of variance explained by a model." PLOS Computational Biology 17, no. 8 (August 4, 2021): e1009212. http://dx.doi.org/10.1371/journal.pcbi.1009212.

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The correlation coefficient squared, r2, is commonly used to validate quantitative models on neural data, yet it is biased by trial-to-trial variability: as trial-to-trial variability increases, measured correlation to a model’s predictions decreases. As a result, models that perfectly explain neural tuning can appear to perform poorly. Many solutions to this problem have been proposed, but no consensus has been reached on which is the least biased estimator. Some currently used methods substantially overestimate model fit, and the utility of even the best performing methods is limited by the lack of confidence intervals and asymptotic analysis. We provide a new estimator, r ^ ER 2, that outperforms all prior estimators in our testing, and we provide confidence intervals and asymptotic guarantees. We apply our estimator to a variety of neural data to validate its utility. We find that neural noise is often so great that confidence intervals of the estimator cover the entire possible range of values ([0, 1]), preventing meaningful evaluation of the quality of a model’s predictions. This leads us to propose the use of the signal-to-noise ratio (SNR) as a quality metric for making quantitative comparisons across neural recordings. Analyzing a variety of neural data sets, we find that up to ∼ 40% of some state-of-the-art neural recordings do not pass even a liberal SNR criterion. Moving toward more reliable estimates of correlation, and quantitatively comparing quality across recording modalities and data sets, will be critical to accelerating progress in modeling biological phenomena.

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Thomas, Stuart C. "The estimation of genetic relationships using molecular markers and their efficiency in estimating heritability in natural populations." Philosophical Transactions of the Royal Society B: Biological Sciences 360, no. 1459 (July 13, 2005): 1457–67. http://dx.doi.org/10.1098/rstb.2005.1675.

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Molecular marker data collected from natural populations allows information on genetic relationships to be established without referencing an exact pedigree. Numerous methods have been developed to exploit the marker data. These fall into two main categories: method of moment estimators and likelihood estimators. Method of moment estimators are essentially unbiased, but utilise weighting schemes that are only optimal if the analysed pair is unrelated. Thus, they differ in their efficiency at estimating parameters for different relationship categories. Likelihood estimators show smaller mean squared errors but are much more biased. Both types of estimator have been used in variance component analysis to estimate heritability. All marker-based heritability estimators require that adequate levels of the true relationship be present in the population of interest and that adequate amounts of informative marker data are available. I review the different approaches to relationship estimation, with particular attention to optimizing the use of this relationship information in subsequent variance component estimation.

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AL-MOUEL, Abdul-Hussein Saber. "COMPARISON OF MINQUE AND SIMPLE ESTIMATOR OF THE ERROR VARIANCE IN THE GAUSS MARKOFF MODEL." Journal of Kufa for Mathematics and Computer 1, no. 1 (April 30, 2010): 39–45. http://dx.doi.org/10.31642/jokmc/2018/010106.

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The problem of estimation of variance components occurs in many areas of research. This paper isdevoted to study the comparison between Minimum Norm Quadratic Unbiased Estimator (MINQUE) andOrdinary Least Square Estimator (OLSE) of s 2 in the Gauss Markoff Model {Y, Xb, s 2V}, under meansquare errors criterion, where the model matrix X need not have full rank and the dispersion matrix V can be singular.A necessary and sufficient condition is obtained for that MINQUE is superior to simple estimator, inparticular, a simple sufficient condition is that the degree of freedom of errors is equal to or greater than 4.

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Journal articles on the topic 'Unbiased Estimation of Estimator Variance'

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