Статті в журналах: "Unbiased ratio estimator"

1

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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2

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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3

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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4

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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5

Jambulingam, Subramani, and Ajith S. Master. "Almost Unbiased Ratio cum Product Estimator for Finite Population Mean with Known Median in Simple Random Sampling." Nepalese Journal of Statistics 1 (December 29, 2017): 1–14. http://dx.doi.org/10.3126/njs.v1i0.18813.

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Introduction: In sampling theory, different procedures are used to obtain the efficient estimator of the population mean. The commonly used method is to obtain the estimator of the population mean is simple random sampling without replacement when there is no auxiliary variable is available. There are methods that use auxiliary information of the study characteristics. If the auxiliary variable is correlated with study variable, number of estimators are widely available in the literature.Objective: This study deals with a new ratio cum product estimator is developed for the estimation of population mean of the study variable with the known median of the auxiliary variable in simple random sampling.Materials and Methods: The bias and mean squared error of proposed estimator are derived and compared with that of the existing estimators by analytically and numerically.Results: The proposed estimator is less biased and mean squared error is less than that of the existing estimators and from the numerical study, under some known natural populations, the bias of proposed estimator is approximately zero and the mean squared error ranged from 6.83 to 66429.21 and percentage relative efficiencies ranged from 103.65 to 2858.75.Conclusion: The proposed estimator under optimum conditions is almost unbiased and performs better than all other existing estimators.Nepalese Journal of Statistics, 2017, Vol. 1, 1-14

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6

Xu, Jianwen, and Hu Yang. "Preliminary test almost unbiased ridge estimator in a linear regression model with multivariate Student-t errors." Acta et Commentationes Universitatis Tartuensis de Mathematica 15, no. 1 (December 11, 2020): 27–43. http://dx.doi.org/10.12697/acutm.2011.15.03.

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In this paper, the preliminary test almost unbiased ridge estimators of the regression coefficients based on the conflicting Wald (W), Likelihood ratio (LR) and Lagrangian multiplier (LM) tests in a multiple regression model with multivariate Student-t errors are introduced when it is suspected that the regression coefficients may be restricted to a subspace. The bias and quadratic risks of the proposed estimators are derived and compared. Sufficient conditions on the departure parameter ∆ and the ridge parameter k are derived for the proposed estimators to be superior to the almost unbiased ridge estimator, restricted almost unbiased ridge estimator and preliminary test estimator. Furthermore, some graphical results are provided to illustrate theoretical results.

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7

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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8

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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9

Rao, T. J., and A. K. P. C. Swain. "A Note on the Hartley-Ross Unbiased Ratio Estimator." Communications in Statistics - Theory and Methods 43, no. 15 (June 30, 2014): 3162–69. http://dx.doi.org/10.1080/03610926.2012.691338.

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10

Ajith S, Master. "Almost Unbiased Ratio Cum Product Estimator for Finite Population Mean with Known Coefficient of Skewness." Journal of Advanced Research in Applied Mathematics and Statistics 2, no. 1&2 (May 10, 2017): 1–9. http://dx.doi.org/10.24321/2455.7021.201701.

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11

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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12

Zarnoch, S. J., and W. A. Bechtold. "Estimating mapped-plot forest attributes with ratios of means." Canadian Journal of Forest Research 30, no. 5 (May 1, 2000): 688–97. http://dx.doi.org/10.1139/x99-247.

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The mapped-plot design utilized by the U.S. Department of Agriculture (USDA) Forest Inventory and Analysis and the National Forest Health Monitoring Programs is described. Data from 2458 forested mapped plots systematically spread across 25 states reveal that 35% straddle multiple conditions. The ratio-of-means estimator is developed as a method to obtain estimates of forest attributes from mapped plots, along with measures of variability useful for constructing confidence intervals. Basic inventory statistics from North and South Carolina were examined to see if these data satisfied the conditions necessary to qualify the ratio of means as the best linear unbiased estimator. It is shown that the ratio-of-means estimator is equivalent to the Horwitz-Thompson, the mean-of-ratios, and the weighted-mean-of-ratios estimators under certain situations.

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13

Parichha, P., K. Basu, A. Bandyopadhyay, and P. Mukhopadhyay. "Development of Efficient Estimation Technique for Population Mean in Two Phase Sampling Using Fuzzy Tools." Journal of Applied Mathematics, Statistics and Informatics 13, no. 2 (December 20, 2017): 5–28. http://dx.doi.org/10.1515/jamsi-2017-0006.

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Abstract The present investigation deals with the problem of estimation of population mean in two-phase (double) sampling. Utilizing information on two auxiliary variables, one chain exponential ratio and regression type estimator has been proposed and its properties are studied under two different structures of twophase sampling. To make the estimator practicable, unbiased version of the proposed strategy has also been developed. The dominance of the suggested estimator over some contemporary estimators of population mean has been established through numerical illustrations carried over the data set of some natural population and artificially generated population. Categorization of the dominance ranges of the proposed estimation strategies are deployed through defuzzification tools, which are followed by suitable recommendations.

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14

Abbasi, Azhar Mehmood, and Muhammad Yousaf Shad. "Sensitive proportion in ranked set sampling." PLOS ONE 16, no. 8 (August 31, 2021): e0256699. http://dx.doi.org/10.1371/journal.pone.0256699.

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This paper considers the concomitant-based rank set sampling (CRSS) for estimation of the sensitive proportion. It is shown that CRSS procedure provides an unbiased estimator of the population sensitive proportion, and it is always more precise than corresponding sample sensitive proportion (Warner SL (1965)) that based on simple random sampling (SRS) without increasing sampling cost. Additionally, a new estimator based on ratio method is introduced using CRSS protocol, preserving the respondent’s confidentiality through a randomizing device. The numerical results of these estimators are obtained by using numerical integration technique. An application to real data is also given to support the methods.

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15

Srivastava, V. K., and R. S. Singh. "Uniformly minimum variance unbiased estimator of efficiency ratio in estimation of normal population mean." Statistics & Probability Letters 10, no. 3 (August 1990): 241–45. http://dx.doi.org/10.1016/0167-7152(90)90081-h.

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16

Zhukov, Olexander, and Ludmila Arabadzhy-Tipenko. "The Ecological Interpretation of Unbiased Estimator for the Taxonomic Ratio: Different Approaches for Local and Regional Flora." Ekológia (Bratislava) 40, no. 4 (December 1, 2021): 348–56. http://dx.doi.org/10.2478/eko-2021-0036.

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Abstract Taxonomic ratio in an ecological context is considered as an indicator of the level of competitive exclusion. In spite of more than a century of discussions on taxonomic ratio, the problem of finding an unbiased estimator for flora characterisation remains unsolved. The traditional form of taxonomic ratio (species/genus or species/families ratio) is biased, which depends on the area of territory for which the floral composition was established. This circumstance makes the taxonomic ratio an inadequate characteristic of the flora. To solve the problem of finding an unbiased estimator for the taxonomic ratio, we have combined two fundamental ecological generalisations. The first is that species that belong to the same genus usually live in similar habitats and have similar morphological features. The struggle for life between species from the same genus is, therefore, more intense than between species from different genera. The second is species–area relationship. We have considered the problem of finding an unbiased taxonomic relationship using the Arrhenius curves to fit species–area relationships. This combination allowed us to find a form of unbiased taxonomic relationship. The example of Cyanophyceae flora shows that this indicator is closely related to a wide range of ecological and biogeographical characteristics of vegetation. The residual of the linear equation of dependence of the logarithm of the number of species on the logarithm of the number of genera is an unbiased indicator of the taxonomic relation, which is independent of the number of genera (or number of families) and the sampling size (or area). An unbiased taxonomic relationship is a characteristic of regional flora, which depends on a wide range of its ecological and biogeographical features.

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17

Pal, Surya K., Sagir A. Mahmud, Madan M. Gupta, Housila P. Singh, and Ramkrishna S. Solanki. "Estimation of finite population mean in sample surveys: A new estimator." Journal of Information & Optimization Sciences 44, no. 1 (2023): 157–69. http://dx.doi.org/10.47974/jios-1304.

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Utilizing supplementary information in simple random sampling, this research paper discussed a new method for finding the finite population mean of a predictive variable, and the properties of the suggested method have been investigated. The suggested estimator’s advantages over traditional estimators are demonstrated using theoretical asymptotic techniques and empirical analysis. The recommended estimator outperforms the customary unbiased, ratio, product, and regression estimators, as well as many other known population mean estimators.

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18

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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19

RIYAZ, SABA, RAFIA JAN, SHOWKAT MAQBOOL, KHALID UL ISLAM RATHER, and T. R. JAN. "A MODIFIED CLASS OF DUAL TO RATIO-TYPE ESTIMATORS FOR ESTIMATING THE POPULATION VARIANCE UNDER SIMPLE RANDOM SAMPLING SCHEME AND ITS APPLICATION TO REAL DATA." Journal of Science and Arts 22, no. 3 (September 30, 2022): 593–604. http://dx.doi.org/10.46939/j.sci.arts-22.3-a06.

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This work is an extension to the work of [1] on ratio estimators of variance, by modification using dual to ratio method. The consistency conditions, bias, mean square error, optimum mean square error and efficiency have been derived and its performance is illustrated using natural populations. It is observed that the proposed class of estimators is most efficient at its optimum value, due to highest percent relative efficiency generated by it, when compared to the usual unbiased estimator for variance.

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20

Solanki, Ramkrishna S., Housila P. Singh, and Anjana Rathour. "An Alternative Estimator for Estimating the Finite Population Mean Using Auxiliary Information in Sample Surveys." ISRN Probability and Statistics 2012 (May 29, 2012): 1–14. http://dx.doi.org/10.5402/2012/657682.

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This paper suggests a class of estimators for estimating the finite population mean of the study variable using known population mean of the auxiliary variable . Asymptotic expressions of bias and variance of the suggested class of estimators have been obtained. Asymptotic optimum estimator (AOE) in the class is identified along with its variance formula. It has been shown that the proposed class of estimators is more efficient than usual unbiased, usual ratio, usual product, Bahl and Tuteja (1991), and Kadilar and Cingi (2003) estimators under some realistic conditions. An empirical study is carried out to judge the merits of suggested estimator over other competitors practically.

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21

Valentine, Harry T., David L. R. Affleck, and Timothy G. Gregoire. "Systematic sampling of discrete and continuous populations: sample selection and the choice of estimator." Canadian Journal of Forest Research 39, no. 6 (June 2009): 1061–68. http://dx.doi.org/10.1139/x09-019.

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Systematic sampling is easy, efficient, and widely used, though it is not generally recognized that a systematic sample may be drawn from the population of interest with or without restrictions on randomization. The restrictions or the lack of them determine which estimators are unbiased, when using the sampling design as the basis for inference. We describe the selection of a systematic sample, with and without restriction, from populations of discrete elements and from linear and areal continuums (continuous populations). We also provide unbiased estimators for both restricted and unrestricted selection. When the population size is known at the outset, systematic sampling with unrestricted selection is most likely the best choice. Restricted selection affords estimation of attribute totals for a population when the population size — for example, the area of an areal continuum — is unknown. Ratio estimation, however, is most likely a more precise option when the selection is restricted and the population size becomes known at the end of the sampling. There is no difference between restricted and unrestricted selection if the sampling interval or grid tessellates the frame in such a way that all samples contain an equal number of measurements. Moreover, all the estimators are unbiased and identical in this situation.

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22

Lee, Young Hoon, Yongdai Kim, and Sara Kim. "Competitive balance with unbalanced schedules." Journal of Quantitative Analysis in Sports 15, no. 3 (August 27, 2019): 239–60. http://dx.doi.org/10.1515/jqas-2017-0100.

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Abstract Many empirical studies on competitive balance (CB) use the ratio of the actual standard deviation to the idealized standard deviation of win percentages (RSD). This paper suggests that empirical studies that use RSD to compare CB among different leagues are invalid, but that RSD may be used for time-series analysis on CB in a league if there are no changes in season length. When schedules are unbalanced and/or include interleague games, the final winning percentage is a biased estimator of the true win probability. This paper takes a mathematical statistical approach to derive an unbiased estimator of within-season CB that can be applied to not only balanced but also unbalanced schedules. Simulations and empirical applications are also presented, which confirm that the debiasing strategy to obtain the unbiased estimator of within-season CB is still effective for unbalanced schedules.

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23

Zheng, Wei Xing. "Study of a least-squares-based algorithm for autoregressive signals subject to white noise." Mathematical Problems in Engineering 2003, no. 3 (2003): 93–101. http://dx.doi.org/10.1155/s1024123x03210012.

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A simple algorithm is developed for unbiased parameter identification of autoregressive (AR) signals subject to white measurement noise. It is shown that the corrupting noise variance, which determines the bias in the standard least-squares (LS) parameter estimator, can be estimated by simply using the expected LS errors when the ratio between the driving noise variance and the corrupting noise variance is known or obtainable in some way. Then an LS-based algorithm is established via the principle of bias compensation. Compared with the other LS-based algorithms recently developed, the introduced algorithm requires fewer computations and has a simpler algorithmic structure. Moreover, it can produce better AR parameter estimates whenever a reasonable guess of the noise variance ratio is available.

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24

Pal, S. K., and H. P. Singh. "Finite Population Mean Estimation through a Two-Parameter Ratio Estimator Using Auxiliary Information in Presence of Non-Response." Journal of Applied Mathematics, Statistics and Informatics 12, no. 2 (December 1, 2016): 5–39. http://dx.doi.org/10.1515/jamsi-2016-0006.

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Abstract In surveys covering human populations it is observed that information in most cases are not obtained at the first attempt even after some callbacks. Such problems come under the category of non-response. Surveys suffer with non-response in various ways. It depends on the nature of required information, either surveys is concerned with general or sensitive issues of a society. Hansen and Hurwitz (1946) have considered the problem of non-response while estimating the population mean by taking a subsample from the non-respondent group with the help of extra efforts and an estimator was suggested by combining the information available from the response and nonresponse groups. We also mention that in survey sampling auxiliary information is commonly used to improve the performance of an estimator of a quantity of interest. For estimating the population mean using auxiliary information in presence of non-response has been discussed by various authors. In this paper, we have developed estimators for estimating the population mean of the variable under interest when there is non-response error in the study as well as in the auxiliary variable. We have studied properties of the suggested estimators under large sample approximation. Comparison of the suggested estimators with usual unbiased estimator reported by Hansen and Hurwitz (1946) and the ratio estimator due to Rao (1986) have been made. The results obtained are illustrated with aid of an empirical study.

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25

Lone, Showkat Ahmad, Mir Subzar, and Ankita Sharma. "Enhanced Estimators of Population Variance with the Use of Supplementary Information in Survey Sampling." Mathematical Problems in Engineering 2021 (April 26, 2021): 1–8. http://dx.doi.org/10.1155/2021/9931217.

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In the present study, we propose the proficient class of estimators of the finite population mean, while incorporating the nonconventional location and nonconventional measures of dispersion with coefficient of variation of the auxiliary variable. Properties associated with the suggested class of improved estimators are derived, and an efficiency comparison with the usual unbiased ratio estimator and other existing estimators under consideration in the present study is established. An empirical study has also been provided to validate the theoretical results. Finally, it is established that the proposed class of estimators of the finite population variance proves to be more efficient than the existing estimators mentioned in this study.

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26

Won, Seok Ho, Whan Woo Kim, Jaemin Ahn, and Deuk-Su Lyu. "An Unbiased Signal-to-Interference Ratio Estimator for the High Speed Downlink Packet Access System." ETRI Journal 25, no. 5 (October 14, 2003): 418–21. http://dx.doi.org/10.4218/etrij.03.0203.0006.

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27

Oyoo, David, Moses Manene, Christopher Ouma, and George Muhua. "ON UNBIASED RATIO ESTIMATOR OF FINITE POPULATION TOTAL IN STRATIFIED RANDOM SAMPLING UNDER NON-RESPONSE." Advances and Applications in Statistics 68, no. 2 (May 20, 2021): 125–34. http://dx.doi.org/10.17654/as068020125.

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28

Chatton, Arthur, Florent Le Borgne, Clémence Leyrat, and Yohann Foucher. "G-computation and doubly robust standardisation for continuous-time data: A comparison with inverse probability weighting." Statistical Methods in Medical Research 31, no. 4 (December 3, 2021): 706–18. http://dx.doi.org/10.1177/09622802211047345.

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In time-to-event settings, g-computation and doubly robust estimators are based on discrete-time data. However, many biological processes are evolving continuously over time. In this paper, we extend the g-computation and the doubly robust standardisation procedures to a continuous-time context. We compare their performance to the well-known inverse-probability-weighting estimator for the estimation of the hazard ratio and restricted mean survival times difference, using a simulation study. Under a correct model specification, all methods are unbiased, but g-computation and the doubly robust standardisation are more efficient than inverse-probability-weighting. We also analyse two real-world datasets to illustrate the practical implementation of these approaches. We have updated the R package RISCA to facilitate the use of these methods and their dissemination.

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29

Baddeley, A. J., and L. M. Cruz-Orive. "The Rao–Blackwell theorem in stereology and some counterexamples." Advances in Applied Probability 27, no. 01 (March 1995): 2–19. http://dx.doi.org/10.1017/s0001867800046188.

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A version of the Rao–Blackwell theorem is shown to apply to most, but not all, stereological sampling designs. Estimators based on random test grids typically have larger variance than quadrat estimators; randoms-dimensional samples are worse than randomr-dimensional samples fors < r.Furthermore, the standard stereological ratio estimators of different dimensions are canonically related to each other by the Rao–Blackwell process. However, there are realistic cases where sampling with a lower-dimensional probeincreasesefficiency. For example, estimators based on (conditionally) non-randomised test point grids may have smaller variance than quadrat estimators. Relative efficiency is related to issues in geostatistics and the theory of wide-sense stationary random fields. A uniform minimum variance unbiased estimator typically does not exist in our context.

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30

Tan, F. E., and M. P. Zeegers. "An asymptotically unbiased estimator of exposed versus non-exposed odds ratio from reported dose-response data." Statistical Methods in Medical Research 10, no. 5 (October 1, 2001): 311–23. http://dx.doi.org/10.1191/096228001680678313.

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31

Tan, Frans ES, and Maurice PA Zeegers. "An asymptotically unbiased estimator of exposed versus non-exposed odds ratio from reported dose-response data." Statistical Methods in Medical Research 10, no. 5 (October 2001): 311–23. http://dx.doi.org/10.1177/096228020101000501.

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32

Quatto, Piero, and Antonella Zambon. "The uniformly minimum variance unbiased estimator of odds ratio in case–control studies under inverse sampling." Statistical Papers 53, no. 2 (June 13, 2010): 305–9. http://dx.doi.org/10.1007/s00362-010-0337-2.

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33

McTague, John Paul. "New and composite point sampling estimates." Canadian Journal of Forest Research 40, no. 11 (November 2010): 2234–42. http://dx.doi.org/10.1139/x10-158.

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A new estimator for basal area is introduced that is based on the concepts of angle count and angle summation sampling. Using the ratio of the angle count basal area factor and the angle summation (borderline) factor, it is possible to estimate stand volume without measuring the diameters and distances of the trees included in the sample. Employing simulation of repeated sampling in a 40 ha forest of known population parameters, it is demonstrated that the new sampling methodology is unbiased and weakly correlated with conventional angle count sampling. Hence, considerable gains in efficiency are made by combining the two sampling methods with composite estimators. Two applications are explored with the new composite point sampling estimates, including the use of the big basal area factor sampling method and critical height sampling using a Max and Burkhart taper formulation.

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34

Baddeley, A. J., and L. M. Cruz-Orive. "The Rao–Blackwell theorem in stereology and some counterexamples." Advances in Applied Probability 27, no. 1 (March 1995): 2–19. http://dx.doi.org/10.2307/1428091.

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A version of the Rao–Blackwell theorem is shown to apply to most, but not all, stereological sampling designs. Estimators based on random test grids typically have larger variance than quadrat estimators; random s-dimensional samples are worse than random r-dimensional samples for s < r. Furthermore, the standard stereological ratio estimators of different dimensions are canonically related to each other by the Rao–Blackwell process. However, there are realistic cases where sampling with a lower-dimensional probe increases efficiency. For example, estimators based on (conditionally) non-randomised test point grids may have smaller variance than quadrat estimators. Relative efficiency is related to issues in geostatistics and the theory of wide-sense stationary random fields. A uniform minimum variance unbiased estimator typically does not exist in our context.

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35

Smith, Nick J., Kim Iles, and Kurt Raynor. "Investigation of Some Sector Sampling Statistical Properties." Forest Science 54, no. 1 (February 1, 2008): 67–76. http://dx.doi.org/10.1093/forestscience/54.1.67.

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Abstract Sector sampling is designed to sample objects in clusters or small, irregularly shaped polygons, such as variable retention patches and associated harvested areas. A number of statistical aspects of sector sampling were examined by using real data and a resampling framework. When the sector angle is selected at random, the probability of sampling each tree is the same; thus, a simple expansion factor method is all that is required to calculate tract totals and mean tree values. Standard variance formulas can then be used. For unit area estimates (such as basal area per hectare) a ratio-of-means estimator balances the areas in different-sized sectors. However, both the ratio-of-means mean and variance may be underestimated. An empirical correction to the biased variance estimator was derived. Alternatively, an unbiased and also more efficient unit area estimate can be made using a random point sector angle selection with a mean-of-ratios method. In this case standard variance formulas can again be used. A systematic sector arrangement reduced variance under an expansion factor but did not reduce variance using a ratio-of-means approach where sector area was already considered.

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36

Huehn, Manfred. "On the bias of recombination fractions, Kosambi's and Haldane's distances based on frequencies of gametes." Genome 54, no. 3 (March 2011): 196–201. http://dx.doi.org/10.1139/g10-109.

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The estimation of recombination frequencies is a crucial step in genetic mapping. For the construction of linkage maps, nonadditive recombination fractions must be transformed into additive map distances. Two of the most commonly used transformations are Kosambi’s and Haldane’s mapping functions. This paper reports on the calculation of the bias associated with estimation of recombination fractions, Kosambi’s distances, and Haldane’s distances. I calculated absolute and relative biases numerically for a wide range of recombination fractions and sample sizes. I assumed that the ratio of recombinant gametes to the total number of gametes can be adequately represented by a binomial function. I found that the bias in recombination fraction estimates is negative, i.e., the estimator is an underestimate. However, significant values were only obtained when recombination fractions were large and sample sizes were small. The relevant estimates of recombination fractions were, therefore, nearly unbiased. Haldane’s and Kosambi’s distances were found to be strongly biased, with positive bias for the most interesting values of recombination fractions and sample sizes. The bias of Kosambi’s distance was considerably smaller than the bias of Haldane’s distance.

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37

Rosic, Maja, Mirjana Simic, Predrag Pejovic, and Milan Bjelica. "Optimal source localization problem based on TOA measurements." Serbian Journal of Electrical Engineering 14, no. 1 (2017): 161–76. http://dx.doi.org/10.2298/sjee1701161r.

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Determining an optimal emitting source location based on the time of arrival (TOA) measurements is one of the important problems in Wireless Sensor Networks (WSNs). The nonlinear least-squares (NLS) estimation technique is employed to obtain the location of an emitting source. This optimization problem has been formulated by the minimization of the sum of squared residuals between estimated and measured data as the objective function. This paper presents a hybridization of Genetic Algorithm (GA) for the determination of the global optimum solution with the local search Newton-Raphson (NR) method. The corresponding Cramer-Rao lower bound (CRLB) on the localization errors is derived, which gives a lower bound on the variance of any unbiased estimator. Simulation results under different signal-to-noise-ratio (SNR) conditions show that the proposed hybrid Genetic Algorithm-Newton-Raphson (GA-NR) improves the accuracy and efficiency of the optimal solution compared to the regular GA.

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38

Corona, Piermaria, and Lorenzo Fattorini. "Area-based lidar-assisted estimation of forest standing volume." Canadian Journal of Forest Research 38, no. 11 (November 2008): 2911–16. http://dx.doi.org/10.1139/x08-122.

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Airborne laser scanning (lidar) technology is increasingly being applied in forest ecosystem surveys. This research note proposes a design-based approach for the lidar-assisted estimation of forest standing volume when ground surveys are performed by means of fixed-area plots. The lidar measurement of the height of the upper canopy (digital crown model) is performed for the whole study area, and the resulting pixel heights are adopted as auxiliary information to couple with the standing volume acquired on the ground by means of sample plots. The ratio estimator for the total volume of the forest is derived in a complete design-based framework together with an unbiased estimator of its sampling variance and the corresponding confidence interval. The proposed procedure has been tested in Bosco della Fontana, a lowland forest in Northern Italy, obtaining a 95% confidence interval for the total volume, which is approximately 2/3 smaller than that obtained by solely using information arising from field plots.

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39

Boruvka, Audrey, and Richard J. Cook. "Sieve estimation in a Markov illness-death process under dual censoring." Biostatistics 17, no. 2 (April 1, 2016): 350–63. http://dx.doi.org/10.1093/biostatistics/kxv042.

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Abstract Semiparametric methods are well established for the analysis of a progressive Markov illness-death process observed up to a noninformative right censoring time. However, often the intermediate and terminal events are censored in different ways, leading to a dual censoring scheme. In such settings, unbiased estimation of the cumulative transition intensity functions cannot be achieved without some degree of smoothing. To overcome this problem, we develop a sieve maximum likelihood approach for inference on the hazard ratio. A simulation study shows that the sieve estimator offers improved finite-sample performance over common imputation-based alternatives and is robust to some forms of dependent censoring. The proposed method is illustrated using data from cancer trials.

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40

Todini, E., F. Pellegrini, and C. Mazzetti. "Influence of parameter estimation uncertainty in Kriging: Part 2 - Test and case study applications." Hydrology and Earth System Sciences 5, no. 2 (June 30, 2001): 225–32. http://dx.doi.org/10.5194/hess-5-225-2001.

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Abstract. The theoretical approach introduced in Part 1 is applied to a numerical example and to the case of yearly average precipitation estimation over the Veneto Region in Italy. The proposed methodology was used to assess the effects of parameter estimation uncertainty on Kriging estimates and on their estimated error variance. The Maximum Likelihood (ML) estimator proposed in Part 1, was applied to the zero mean deviations from yearly average precipitation over the Veneto Region in Italy, obtained after the elimination of a non-linear drift with elevation. Three different semi-variogram models were used, namely the exponential, the Gaussian and the modified spherical, and the relevant biases as well as the increases in variance have been assessed. A numerical example was also conducted to demonstrate how the procedure leads to unbiased estimates of the random functions. One hundred sets of 82 observations were generated by means of the exponential model on the basis of the parameter values identified for the Veneto Region rainfall problem and taken as characterising the true underlining process. The values of parameter and the consequent cross-validation errors, were estimated from each sample. The cross-validation errors were first computed in the classical way and then corrected with the procedure derived in Part 1. Both sets, original and corrected, were then tested, by means of the Likelihood ratio test, against the null hypothesis of deriving from a zero mean process with unknown covariance. The results of the experiment clearly show the effectiveness of the proposed approach. Keywords: yearly rainfall, maximum likelihood, Kriging, parameter estimation uncertainty

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41

Búrquez, Alberto, and Angelina Martínez-Yrízar. "Accuracy and bias on the estimation of aboveground biomass in the woody vegetation of the Sonoran Desert." Botany 89, no. 9 (September 2011): 625–33. http://dx.doi.org/10.1139/b11-050.

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We developed allometric regressions for predicting aboveground biomass (AGB) in the Sonoran Desert. Information on canopy cover and height was collected and used to predict AGB from plant dimensions in twenty 25 m2plots that were also fully harvested. The comparison of these two methods showed that allometric equations without correction for bias led to gross AGB underestimation (four times lower than the true values for uncorrected logarithmic allometric equations). Among the tested correction factors, the ratio estimator highly reduced bias and increased accuracy. Validation of allometric estimates with whole-plot harvesting defined the best equation and the least biased correction factor. However, simple nonlinear power functions also gave accurate and unbiased estimates of AGB. We recommend the use of nonlinear models in lieu of traditional logarithm-transformed models. Correction for bias and field verification should be considered in allometric regressions used to predict AGB. In the absence of validation by direct biomass measurements, allometric predictions derived from linearization of ln-transformed data should be taken with care.

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42

Dong, Gaohong, Lu Mao, Bo Huang, Margaret Gamalo-Siebers, Jiuzhou Wang, GuangLei Yu, and David C. Hoaglin. "The inverse-probability-of-censoring weighting (IPCW) adjusted win ratio statistic: an unbiased estimator in the presence of independent censoring." Journal of Biopharmaceutical Statistics 30, no. 5 (June 17, 2020): 882–99. http://dx.doi.org/10.1080/10543406.2020.1757692.

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43

Gay, Roger. "Premium Calculation for Fat-tailed Risk." ASTIN Bulletin 35, no. 01 (May 2005): 163–88. http://dx.doi.org/10.2143/ast.35.1.583171.

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When insurance claims are governed by fat-tailed distributions considerable uncertainty about the value of the tail-index is often inescapable. In this paper, using the theory of risk aversion, a new premium principle (the power principle – analogous to the exponential principle for thin-tailed claims) is established and its properties investigated. Applied to claims arising from generalized Pareto distributions, the resultant premium is shown to be the ratio of the two largest expected claims, for which the ratio of the actual claims is an unbiased as well as a consistent estimator. Whereas thin-tailed claim premiums are determined largely by the first two moments of the claims distribution, fat-tailed claim premiums are determined by the first two extremes. The context of risk-aversion leads to a natural model for incorporating tail-index uncertainty into premiums, which nevertheless leaves the basic ratio structure unaltered. To illustrate the theory, possible ‘premiums’ for US hurricane data are examined, which utilize the consistent pattern of observed extremes.

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44

Gay, Roger. "Premium Calculation for Fat-tailed Risk." ASTIN Bulletin 35, no. 1 (May 2005): 163–88. http://dx.doi.org/10.1017/s0515036100014112.

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When insurance claims are governed by fat-tailed distributions considerable uncertainty about the value of the tail-index is often inescapable. In this paper, using the theory of risk aversion, a new premium principle (the power principle – analogous to the exponential principle for thin-tailed claims) is established and its properties investigated. Applied to claims arising from generalized Pareto distributions, the resultant premium is shown to be the ratio of the two largest expected claims, for which the ratio of the actual claims is an unbiased as well as a consistent estimator. Whereas thin-tailed claim premiums are determined largely by the first two moments of the claims distribution, fat-tailed claim premiums are determined by the first two extremes. The context of risk-aversion leads to a natural model for incorporating tail-index uncertainty into premiums, which nevertheless leaves the basic ratio structure unaltered. To illustrate the theory, possible ‘premiums’ for US hurricane data are examined, which utilize the consistent pattern of observed extremes.

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45

Li, Jiaqi, Anil Vachani, Andrew Epstein, and Nandita Mitra. "A doubly robust approach for cost–effectiveness estimation from observational data." Statistical Methods in Medical Research 27, no. 10 (February 27, 2017): 3126–38. http://dx.doi.org/10.1177/0962280217693262.

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Estimation of common cost–effectiveness measures, including the incremental cost–effectiveness ratio and the net monetary benefit, is complicated by the need to account for informative censoring and inherent skewness of the data. In addition, since the two components of these measures, medical costs and survival are often collected from observational claims data, one must account for potential confounders. We propose a novel doubly robust, unbiased estimator for cost–effectiveness based on propensity scores that allow the incorporation of cost history and time-varying covariates. Further, we use an ensemble machine learning approach to obtain improved predictions from parametric and non-parametric cost and propensity score models. Our simulation studies demonstrate that the proposed doubly robust approach performs well even under mis-specification of either the propensity score model or the outcome model. We apply our approach to a cost–effectiveness analysis of two competing lung cancer surveillance procedures, CT vs. chest X-ray, using SEER-Medicare data.

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46

Hyun, Myung Jin, Jongseok Won, Dong Han Choi, Howon Lee, Yeonjung Lee, Charity Mijin Lee, Chan Hong Park, and Jae Hoon Noh. "A CHEMTAX Study Based on Picoeukaryotic Phytoplankton Pigments and Next-Generation Sequencing Data from the Ulleungdo–Dokdo Marine System of the East Sea (Japan Sea): Improvement of Long-Unresolved Underdetermined Bias." Journal of Marine Science and Engineering 10, no. 12 (December 10, 2022): 1967. http://dx.doi.org/10.3390/jmse10121967.

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The CHEMTAX program has been widely used to estimate community composition based on major pigment concentrations in seawater. However, because CHEMTAX is an underdetermined optimization algorithm, underdetermined bias has remained an unsolved problem since its development in 1996. The risk of producing biased results increases when analyzing the picophytoplankton community; therefore, this study tested a new method for avoiding biased CHEMTAX results using the picophytoplankton community around the East Sea (Japan Sea). This method involves building a linear model between pigment concentration data and community composition data based on DNA sequencing to predict the pigment range for each operational taxonomic unit, based on the 95% prediction interval. Finally, the range data are transformed into an initial ratio and ratio limits for CHEMTAX analysis. Three combinations of initial ratios and ratio limits were tested to determine whether the modeled initial ratio and ratio limit could prevent underdetermined bias in the CHEMTAX estimates; these combinations were the modeled initial ratio and ratio limit, the modeled initial ratio with a default ratio limit of 500 s, and an initial ratio from previous research with the default ratio limit. The final ratio and composition data for each combination were compared with Bayesian compositional estimator-based final ratio and composition data, which are robust against underdetermined bias. Only CHEMTAX analysis using the modeled initial ratio and ratio limit was unbiased; all other combinations showed significant signs of bias. Therefore, the findings in this study indicate that ratio limits and the initial ratio are equally important in the CHEMTAX analysis of biased datasets. Moreover, we obtained statistically supported initial ratios and ratio limits through linear modeling of pigment concentrations and 16s rDNA composition data.

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47

Jha, Mayank Kumar, Sanku Dey, and Yogesh Mani Tripathi. "Reliability estimation in a multicomponent stress–strength based on unit-Gompertz distribution." International Journal of Quality & Reliability Management 37, no. 3 (December 25, 2019): 428–50. http://dx.doi.org/10.1108/ijqrm-04-2019-0136.

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Purpose The purpose of this paper is to estimate the multicomponent reliability by assuming the unit-Gompertz (UG) distribution. Both stress and strength are assumed to have an UG distribution with common scale parameter. Design/methodology/approach The reliability of a multicomponent stress–strength system is obtained by the maximum likelihood (MLE) and Bayesian method of estimation. Bayes estimates of system reliability are obtained by using Lindley’s approximation and Metropolis–Hastings (M–H) algorithm methods when all the parameters are unknown. The highest posterior density credible interval is obtained by using M–H algorithm method. Besides, uniformly minimum variance unbiased estimator and exact Bayes estimates of system reliability have been obtained when the common scale parameter is known and the results are compared for both small and large samples. Findings Based on the simulation results, the authors observe that Bayes method provides better estimation results as compared to MLE. Proposed asymptotic and HPD intervals show satisfactory coverage probabilities. However, average length of HPD intervals tends to remain shorter than the corresponding asymptotic interval. Overall the authors have observed that better estimates of the reliability may be achieved when the common scale parameter is known. Originality/value Most of the lifetime distributions used in reliability analysis, such as exponential, Lindley, gamma, lognormal, Weibull and Chen, only exhibit constant, monotonically increasing, decreasing and bathtub-shaped hazard rates. However, in many applications in reliability and survival analysis, the most realistic hazard rates are upside-down bathtub and bathtub-shaped, which are found in the unit-Gompertz distribution. Furthermore, when reliability is measured as percentage or ratio, it is important to have models defined on the unit interval in order to have plausible results. Therefore, the authors have studied the multicomponent stress–strength reliability under the unit-Gompertz distribution by comparing the MLEs, Bayes estimators and UMVUEs.

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48

Ramsey, Dave, Murray Efford, Steve Ball, and Graham Nugent. "The evaluation of indices of animal abundance using spatial simulation of animal trapping." Wildlife Research 32, no. 3 (2005): 229. http://dx.doi.org/10.1071/wr03119.

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We apply a new algorithm for spatially simulating animal trapping that utilises a detection function and allows for competition between animals and traps. Estimates of the parameters of the detection function from field studies allowed us to simulate realistically the expected range of detection probabilities of brushtail possums caught in traps. Using this model we evaluated a common index of population density of brushtail possums based on the percentage of leg-hold traps catching possums. Using field estimates of the parameters of the detection function, we simulated the relationship between the trap-catch index and population density. The relationship was linear up to densities of 10 possums ha–1. We also investigated the accuracy (bias and precision) of the trap-catch index for possums to estimate relative changes in population density (relative abundance) under conditions of varying detection probability, and compared these results with those obtained using a removal estimate of the population in the vicinity of trap lines. The ratio of trap-catch indices was a more precise estimator of relative abundance than the ratio of removal estimates but was positively biased (i.e. overestimated relative abundance). In contrast, the ratio of removal estimates was relatively unbiased but imprecise. Despite the positive bias, the trap-catch index had a higher power to determine the correct ranking between population densities than the removal estimate. Although varying detection probability can bias estimates of relative abundance using indices, we show that the potential for bias to lead to an incorrect result is small for indices of brushtail possum density based on trapping.

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49

Shaik, Muneer, and Maheswaran S. "Evidence of excess volatility based on a new robust volatility ratio." Journal of Economic Studies 45, no. 4 (September 10, 2018): 855–75. http://dx.doi.org/10.1108/jes-06-2017-0150.

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Purpose The purpose of this paper is twofold: first, to propose a new robust volatility ratio (RVR) that compares the intraday high–low volatility with that of the intraday open–close volatility estimator; and second, to empirically test the proposed RVR on the cross-sectional (CS) average of the constituent stocks of India’s BSE Sensex and US’s Dow Jones Industrial Average index to find the evidence of “excess volatility.” Design/methodology/approach The authors model the proposed RVR by assuming the logarithm of the price process to follow the Brownian motion. The authors have theoretically shown that the RVR is unbiased in the case of zero drift parameter. Moreover, the RVR is found to be an even function of the non-zero drift parameter. Findings The empirical results show that the analysis based on the RVR supports the existence of “excess volatility” in the CS average of the constituent stocks of India’s BSE Sensex and US’s Dow Jones index. In particular, the authors have observed that the CS average of individual constituent stocks of BSE Sensex is found to be more excessively volatile than the US’s Dow Jones index during the period of the study from January 2008 to September 2016, based on multiple k-day time window analysis. Practical implications The study has implications for the policy makers and practitioners who would like to understand the volatility behavior in the asset returns based on the RVR of this study. In general, the proposed model can be used as a specification tool to find whether the stock prices follow the random walk behavior or excessively volatile. Originality/value The authors contribute to the existing volatility literature in finance by proposing a new RVR based on extreme values of asset prices and absolute returns. The authors implement the bootstrap technique on RVR to find the estimates of mean and standard error for multiple k-day time windows. The RVR can capture the excess volatility by comparing two independent volatility estimators. This is possibly the first study to find the CS average of all the constituent stocks of BSE Sensex based on the RVR.

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50

Guloglu, Bülent, Sinem Guler Kangalli Uyar, and Umut Uyar. "Dynamic Quantile Panel Data Analysis of Stock Returns Predictability." International Journal of Economics and Finance 8, no. 2 (January 24, 2016): 115. http://dx.doi.org/10.5539/ijef.v8n2p115.

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<p>This paper analyses the effect of financial ratios on stock returns using quantile regression for dynamic panel data with fixed effects. Eighty three firms of manufacturing industry, which were traded on the Borsa Istanbul for 2000-2014 period, are covered in the study. The most of financial variables have heterogeneous structure so they generally include extreme values. Thus, panel quantile regression technique, suggested by Koenker (2004), is used. Since the technique yields robust estimator in the case of extreme values the Gaussian estimators will be biased and not efficient. The sensitivity of relationship, on the other hand, can be studied for different parts of the stock returns’ conditional distribution by using quantile regression technique. However, because of that the lagged of dependent variable is used as an explanatory variable in dynamic panel models, fixed effect estimators will be biased. Thereby, in this study the instrumental variable approach suggested by Chernozhukov and Hansen (2006) is used to produce unbiased and consistent estimators.</p>The results show that the stock returns respond to the changes on the financial leverage ratio, the dividend yield, the market-to-book value ratio, financial beta and the total active profitability variables differently for the different parts of the stock returns’ conditional distribution. They also indicate that, at high quantiles, return fluctuations in the current period will be more effective for investors’ transaction attitudes on stocks for the next period.

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