Статті в журналах: "Generalised regression estimators"

1

Zhang, Li-Chun. "Generalised Regression Estimation Given Imperfectly Matched Auxiliary Data." Journal of Official Statistics 37, no. 1 (March 1, 2021): 239–55. http://dx.doi.org/10.2478/jos-2021-0010.

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Abstract Generalised regression estimation allows one to make use of available auxiliary information in survey sampling. We develop three types of generalised regression estimator when the auxiliary data cannot be matched perfectly to the sample units, so that the standard estimator is inapplicable. The inference remains design-based. Consistency of the proposed estimators is either given by construction or else can be tested given the observed sample and links. Mean square errors can be estimated. A simulation study is used to explore the potentials of the proposed estimators.

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2

Wada, Kazumi, Keiichiro Sakashita, and Hiroe Tsubaki. "Robust Estimation for a Generalised Ratio Model." Austrian Journal of Statistics 50, no. 1 (February 3, 2021): 74–87. http://dx.doi.org/10.17713/ajs.v50i1.994.

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It is known that data such as business sales and household income need data transformation prior to regression estimate as the data has a homoscedastic error. However, data transformations make the estimation of mean and total unstable. Therefore, the ratio model is often used for imputation in the field of official statistics to avoid the problem. Our study aims to robustify the estimator following the ratio model by means of M-estimation. Reformulation of the conventional ratio model with homoscedastic quasi-error term provides quasi-residuals which can be used as a measure of outlyingness as same as a linear regression model. A generalisation of the model, which accommodates varied error terms with different heteroscedasticity, is also proposed. Functions for robustified estimators of the generalised ratio model are implemented by the iterative re-weighted least squares algorithm in R environment and illustrated using random datasets. Monte Carlo simulation confirms accuracy of the proposed estimators, as well as their computational efficiency. A comparison of the scale parameters between the average absolute deviation (AAD) and median absolute deviation (MAD) is made regarding Tukey's biweight function. The results with Huber's weight function are also provided for reference. The proposed robust estimator of the generalised ratio model is used for imputation of major corporate accounting items of the 2016 Economic Census for Business Activity in Japan.

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3

Mohammed, M. A., Huda M. Alshanbari, and Abdal-Aziz H. El-Bagoury. "Application of the LINEX Loss Function with a Fundamental Derivation of Liu Estimator." Computational Intelligence and Neuroscience 2022 (March 14, 2022): 1–9. http://dx.doi.org/10.1155/2022/2307911.

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For a variety of well-known approaches, optimum predictors and estimators are determined in relation to the asymmetrical LINEX loss function. The applications of an iteratively practicable lowest mean squared error estimation of the regression disturbance variation with the LINEX loss function are discussed in this research. This loss is a symmetrical generalisation of the quadratic loss function. Whenever the LINEX loss function is applied, we additionally look at the risk performance of the feasible virtually unbiased generalised Liu estimator and practicable generalised Liu estimator. Whenever the variation σ 2 is specified, we get all acceptable linear estimation in the class of linear estimation techniques, and when σ 2 is undetermined, we get all acceptable linear estimation in the class of linear estimation techniques. During position transformations, the proposed Liu estimators are stable. The estimators’ biases and hazards are calculated and evaluated. We utilize an asymmetrical loss function, the LINEX loss function, to calculate the actual hazards of several error variation estimators. The employment of δ P σ , which is easy to use and maximin, is recommended in the conclusions.

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4

Laroussi, Ilhem. "A generalised censored least squares and smoothing spline estimators of regression function." International Journal of Mathematics in Operational Research 20, no. 4 (2021): 506. http://dx.doi.org/10.1504/ijmor.2021.120102.

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5

Sutradhar, B. "Miscellanea. On the efficiency of regression estimators in generalised linear models for longitudinal data." Biometrika 86, no. 2 (June 1, 1999): 459–65. http://dx.doi.org/10.1093/biomet/86.2.459.

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6

Khare, B. B., and Sanjay Kumar. "Generalised chain ratio-in-regression estimators for population mean using two-phase sampling in the presence of non-response." Journal of Information and Optimization Sciences 36, no. 4 (June 9, 2015): 317–38. http://dx.doi.org/10.1080/02522667.2014.926706.

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7

Slaoui, Y., and A. Jmaei. "Recursive and non-recursive regression estimators using Bernstein polynomials." Theory of Stochastic Processes 26(42), no. 1 (December 27, 2022): 60–95. http://dx.doi.org/10.37863/tsp-2899660400-77.

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If a regression function has a bounded support, the kernel estimates often exceed the boundaries and are therefore biased on and near these limits. In this paper, we focus on mitigating this boundary problem. We apply Bernstein polynomials and the Robbins-Monro algorithm to construct a non-recursive and recursive regression estimator. We study the asymptotic properties of these estimators, and we compare them with those of the Nadaraya-Watson estimator and the generalized Révész estimator introduced by [21]. In addition, through some simulation studies, we show that our non-recursive estimator has the lowest integrated root mean square error (ISE) in most of the considered cases. Finally, using a set of real data, we demonstrate how our non-recursive and recursive regression estimators can lead to very satisfactory estimates, especially near the boundaries.

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8

DEVITA, HANY, I. KOMANG GDE SUKARSA, and I. PUTU EKA N. KENCANA. "KINERJA JACKKNIFE RIDGE REGRESSION DALAM MENGATASI MULTIKOLINEARITAS." E-Jurnal Matematika 3, no. 4 (November 28, 2014): 146. http://dx.doi.org/10.24843/mtk.2014.v03.i04.p077.

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Ordinary least square is a parameter estimations for minimizing residual sum of squares. If the multicollinearity was found in the data, unbias estimator with minimum variance could not be reached. Multicollinearity is a linear correlation between independent variabels in model. Jackknife Ridge Regression(JRR) as an extension of Generalized Ridge Regression (GRR) for solving multicollinearity. Generalized Ridge Regression is used to overcome the bias of estimators caused of presents multicollinearity by adding different bias parameter for each independent variabel in least square equation after transforming the data into an orthoghonal form. Beside that, JRR can reduce the bias of the ridge estimator. The result showed that JRR model out performs GRR model.

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9

Shaheen, Nazia, Muhammad Nouman Qureshi, Osama Abdulaziz Alamri, and Muhammad Hanif. "Optimized inferences of finite population mean using robust parameters in systematic sampling." PLOS ONE 18, no. 1 (January 23, 2023): e0278619. http://dx.doi.org/10.1371/journal.pone.0278619.

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In this article, we have proposed a generalized estimator for mean estimation by combining the ratio and regression methods of estimation in the presence of auxiliary information using systematic sampling. We incorporated some robust parameters of the auxiliary variable to obtain precise estimates of the proposed estimator. The mathematical expressions for bias and mean square error of proposed the estimator are derived under large sample approximation. Many other generalized ratio and product-type estimators are obtained from the proposed estimator using different choices of scalar constants. Some special cases are also discussed in which the proposed generalized estimator reduces to the usual mean, classical ratio, product, and regression type estimators. Mathematical conditions are obtained for which the proposed estimator will perform more precisely than the challenging estimators mentioned in this article. The efficiency of the proposed estimator is evaluated using four populations. Results showed that the proposed estimator is efficient and useful for survey sampling in comparison to the other existing estimators.

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10

SÖKÜT AÇAR, Tuğba. "Kibria-Lukman Estimator for General Linear Regression Model with AR(2) Errors: A Comparative Study with Monte Carlo Simulation." Journal of New Theory, no. 41 (December 31, 2022): 1–17. http://dx.doi.org/10.53570/jnt.1139885.

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The sensitivity of the least-squares estimation in a regression model is impacted by multicollinearity and autocorrelation problems. To deal with the multicollinearity, Ridge, Liu, and Ridge-type biased estimators have been presented in the statistical literature. The recently proposed Kibria-Lukman estimator is one of the Ridge-type estimators. The literature has compared the Kibria-Lukman estimator with the others using the mean square error criterion for the linear regression model. It was achieved in a study conducted on the Kibria-Lukman estimator's performance under the first-order autoregressive erroneous autocorrelation. When there is an autocorrelation problem with the second-order, evaluating the performance of the Kibria-Lukman estimator according to the mean square error criterion makes this paper original. The scalar mean square error of the Kibria-Lukman estimator under the second-order autoregressive error structure was evaluated using a Monte Carlo simulation and two real examples, and compared with the Generalized Least-squares, Ridge, and Liu estimators. The findings revealed that when the variance of the model was small, the mean square error of the Kibria-Lukman estimator gave very close values with the popular biased estimators. As the model variance grew, Kibria-Lukman did not give fairly similar values with popular biased estimators as in the model with small variance. However, according to the mean square error criterion the Kibria-Lukman estimator outperformed the Generalized Least-Squares estimator in all possible cases.

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11

Moyo, Vusani, Hendrik Wolmarans, and Leon Brummer. "Trade-Off Or Pecking Order: Evidence From South African Manufacturing, Mining, And Retail Firms." International Business & Economics Research Journal (IBER) 12, no. 8 (July 29, 2013): 927. http://dx.doi.org/10.19030/iber.v12i8.7989.

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This study tests the trade-off and pecking order hypotheses of corporate financing decisions and estimates the speed of adjustment toward target leverage using a cross-section of 42 manufacturing, 24 mining and 21 retail firms listed on the Johannesburg Stock Exchange (JSE) for the period 2000-2010. It uses the generalised least squares (GLS) random effects, maximum likelihood (ML) random effects, fixed effects, time series regression, Arellano and Bond (1991), Blundell and Bond (1998) and random effects Tobit estimators to fit the two versions of the partial adjustment models. The study finds that leverage is positively correlated to profitability and this supports the trade-off theory. The trade-off theory is further supported by the negative correlation on non-debt tax shields. Consistent with the pecking order theory, capital expenditure and growth rate are positively correlated to leverage while asset tangibility is inversely related to leverage. The negative correlation on financial distress and the positive correlation on dividends paid support both the pecking order and trade-off theories. These results are consistent with the view that the pecking order and trade-off theories are non-mutual exclusive in explaining the financing decisions of firms. The results also show that South African manufacturing, mining and retail firms do have target leverage ratios and the true speed of adjustment towards target leverage is 57.64% for book-to-debt ratio and 42.44% for market-to-debt ratio.

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12

Obenchain, Robert L. "Efficient Generalized Ridge Regression." Open Statistics 3, no. 1 (January 1, 2022): 1–18. http://dx.doi.org/10.1515/stat-2022-0108.

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Abstract The original ridge estimator of the unknown p×1 vector of β-coefficients in a linear model used a single scalar, k, to determine a point on a shrinkage path of finite length that extends from the Ordinary Least Squares estimator, ^β 0, to the shrinkage terminus (usually ^β ≡ 0). Generalized ridge estimators use two or more parameters to determine not only the shape of their shrinkage path but also a specific point on that path. The efficient generalized ridge regression path proposed here is a continuous two-piece linear function that (1) starts at ^β 0, the Best Linear Unbiased Estimator, (2) has its interior knot at the ^ β-estimator with Maximum Likelihood of achieving overall minimum MSE risk under normal distribution-theory, and (3) ends at the shrinkage terminus. This new path is efficient in the senses that it is the shortest path and, at least when p > 2, essentially the only known shrinkage path that always contains the ^ β-vector that is most likely to be optimally biased. Functions in R-packages freely distributed via CRAN perform the calculations and produce the graphics used here to illustrate shrinkage concepts by interpreting ridge Trace diagnostic plots. These new concepts and visual tools provide invaluable data-analytic insights and improved self-confidence to applied researchers and data scientists fitting linear models when p, the number of non-constant X-predictor variables in the model, is strictly less than the number of observations available.

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13

Youssef, Ahmed H., Mohamed R. Abonazel, and Amr R. Kamel. "Efficiency Comparisons of Robust and Non-Robust Estimators for Seemingly Unrelated Regressions Model." WSEAS TRANSACTIONS ON MATHEMATICS 21 (May 6, 2022): 218–44. http://dx.doi.org/10.37394/23206.2022.21.28.

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This paper studies and reviews several procedures for developing robust regression estimators of the seemingly unrelated regressions (SUR) model, when the variables are affected by outliers. To compare the robust estimators (M-estimation, S-estimation, and MM-estimation) with non-robust (traditional maximum likelihood and feasible generalized least squares) estimators of this model with outliers, the Monte Carlo simulation study has been performed. The simulation factors of our study are the number of equations in the system, the number of observations, the contemporaneous correlation among equations, the number of regression parameters, and the percentages of outliers in the dataset. The simulation results showed that, based on total mean squared error (TMSE), total mean absolute error (TMAE) and relative absolute bias (RAB) criteria, robust estimators give better performance than non-robust estimators; specifically, the MM-estimator is more efficient than other estimators. While when the dataset does not contain outliers, the results showed that the unbiased SUR estimator (feasible generalized least squares estimator) is more efficient than other estimators.

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14

Özbay, Nimet, Issam Dawoud, and Selahattin Kaçıranlar. "Feasible Generalized Stein-Rule Restricted Ridge Regression Estimators." Journal of Applied Mathematics, Statistics and Informatics 13, no. 1 (May 24, 2017): 77–97. http://dx.doi.org/10.1515/jamsi-2017-0005.

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Abstract Several versions of the Stein-rule estimators of the coefficient vector in a linear regression model are proposed in the literature. In the present paper, we propose new feasible generalized Stein-rule restricted ridge regression estimators to examine multicollinearity and autocorrelation problems simultaneously for the general linear regression model, when certain additional exact restrictions are placed on these coefficients. Moreover, a Monte Carlo simulation experiment is performed to investigate the performance of the proposed estimator over the others.

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15

Kızılarslan, Şaban, and Ceren Camkıran. "Comparison of robust logistic regression estimators for variables with generalized extreme value distributions." Model Assisted Statistics and Applications 16, no. 3 (August 27, 2021): 177–87. http://dx.doi.org/10.3233/mas-210531.

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The aim of this study is to compare the performance of robust estimators in the presence of explanatory variables with Generalized Extreme Value (GEV) distributions in the logistic regression model. Existence of extreme values in the logistic regression model negatively affects the bias and effectiveness of classical Maximum Likelihood (ML) estimators. For this reason, robust estimators that are less sensitive to extreme values have been developed. Random variables with extreme values may be fit in one of specific distributions. In study, the GEV distribution family was examined and five robust estimators were compared for the Fréchet, Gumbel and Weibull distributions. To the simulation results, the CUBIF estimator is prominent according to both bias and efficiency criteria for small samples. In medium and large samples, while the MALLOWS estimator has the minimum bias, the CUBIF estimator has the best efficiency. The same results apply for different contamination ratios and different scale parameter values of the distributions. Simulation findings were supported by a meteorological real data application.

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16

Lukman, Adewale F., B. M. Golam Kibria, Cosmas K. Nziku, Muhammad Amin, Emmanuel T. Adewuyi, and Rasha Farghali. "K-L Estimator: Dealing with Multicollinearity in the Logistic Regression Model." Mathematics 11, no. 2 (January 9, 2023): 340. http://dx.doi.org/10.3390/math11020340.

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Multicollinearity negatively affects the efficiency of the maximum likelihood estimator (MLE) in both the linear and generalized linear models. The Kibria and Lukman estimator (KLE) was developed as an alternative to the MLE to handle multicollinearity for the linear regression model. In this study, we proposed the Logistic Kibria-Lukman estimator (LKLE) to handle multicollinearity for the logistic regression model. We theoretically established the superiority condition of this new estimator over the MLE, the logistic ridge estimator (LRE), the logistic Liu estimator (LLE), the logistic Liu-type estimator (LLTE) and the logistic two-parameter estimator (LTPE) using the mean squared error criteria. The theoretical conditions were validated using a real-life dataset, and the results showed that the conditions were satisfied. Finally, a simulation and the real-life results showed that the new estimator outperformed the other considered estimators. However, the performance of the estimators was contingent on the adopted shrinkage parameter estimators.

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17

Phillips, Peter C. B. "Robust Nonstationary Regression." Econometric Theory 11, no. 5 (October 1995): 912–51. http://dx.doi.org/10.1017/s0266466600009920.

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This paper provides a robust statistical approach to nonstationary time series regression and inference. Fully modified extensions of traditional robust statistical procedures are developed that allow for endogeneities in the nonstationary regressors and serial dependence in the shocks that drive the regressors and the errors that appear in the equation being estimated. The suggested estimators involve semiparametric corrections to accommodate these possibilities, and they belong to the same family as the fully modified least-squares (FM-OLS) estimator of Phillips and Hansen (1990, Review of Economic Studies 57,99–125). Specific attention is given to fully modified least absolute deviation (FM-LAD) estimation and fully modified M (FM-M) estimation. The criterion function for LAD and some M-estimators is not always smooth, and this paper develops generalized function methods to cope with this difficulty in the asymptotics. The results given here include a strong law of large numbers and some weak convergence theory for partial sums of generalized functions of random variables. The limit distribution theory for FM-LAD and FM-M estimators that is developed includes the case of finite variance errors and the case of heavytailed (infinite variance) errors. Some simulations and a brief empirical illustration are reported.

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18

McDonald, James B., and Whitney K. Newey. "Partially Adaptive Estimation of Regression Models via the Generalized T Distribution." Econometric Theory 4, no. 3 (December 1988): 428–57. http://dx.doi.org/10.1017/s0266466600013384.

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This paper considers M-estimators of regression parameters that make use of a generalized functional form for the disturbance distribution. The family of distributions considered is the generalized t (GT), which includes the power exponential or Box-Tiao, normal, Laplace, and t distributions as special cases. The corresponding influence function is bounded and redescending for finite “degrees of freedom.” The regression estimators considered are those that maximize the GT quasi-likelihood, as well as one-step versions. Estimators of the parameters of the GT distribution and the effect of such estimates on the asymptotic efficiency of the regression estimates are discussed. We give a minimum-distance interpretation of the choice of GT parameter estimate that minimizes the asymptotic variance of the regression parameters.

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19

APANTAKU, F. S., O. M. OLAYIWOLA, A. O. AJAYI, and O. S. JAIYEOLA. "A MODIFIED GENERALIZED CHAIN RATIO IN REGRESSION ESTIMATOR." Journal of Natural Sciences Engineering and Technology 19, no. 1 (December 2, 2021): 1–7. http://dx.doi.org/10.51406/jnset.v19i1.2087.

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Generalized Chain ratio in regression type estimator is efficient for estimating the population mean. Many authors have derived a Generalized Chain ratio in regression type estimator. However, the computation of its Mean Square Error (MSE) is cumbersome based on the fact that several iterations have to be done, hence the need for a modified generalized chain ratio in regression estimator with lower MSE. This study proposed a modified generalized chain ratio in regression estimator which is less cumbersome in its computation. Two data sets were used in this study. The first data were on tobacco production by tobacco producing countries with yield of tobacco (variable of interest), area of land and production in metric tonnes as the auxiliary variables. The second data were the number of graduating pupils (variable of interest) in Ado-Odo/Ota local government, Ogun state with the number of enrolled pupils in primaries one and five as the auxiliary variables. The mean square errors in the existing and proposed estimators for various values of alpha were derived and relative efficiency was determined. The MSE for the existing estimator of tobacco production gave six values 0.0080, 0.0079, 0.0080, 0.0082, 0.0087 and 0.0093 with 0.0079 as the minimum while the proposed estimator gave 0.0054. The MSEs for the existing estimator for the graduating pupils were 20.73, 11.08, 7.49, 9.96, 18.50 and 33.10 with 7.49 as the minimum while the proposed was 6.52. The results of this study showed that the proposed estimator gave lower MSE for the two data sets, hence it is more efficient.

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20

Aladeitan, Benedicta B., Olukayode Adebimpe, Adewale F. Lukman, Olajumoke Oludoun, and Oluwakemi E. Abiodun. "Modified Kibria-Lukman (MKL) estimator for the Poisson Regression Model: application and simulation." F1000Research 10 (December 14, 2021): 548. http://dx.doi.org/10.12688/f1000research.53987.2.

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Background: Multicollinearity greatly affects the Maximum Likelihood Estimator (MLE) efficiency in both the linear regression model and the generalized linear model. Alternative estimators to the MLE include the ridge estimator, the Liu estimator and the Kibria-Lukman (KL) estimator, though literature shows that the KL estimator is preferred. Therefore, this study sought to modify the KL estimator to mitigate the Poisson Regression Model with multicollinearity. Methods: A simulation study and a real-life study was carried out and the performance of the new estimator was compared with some of the existing estimators. Results: The simulation result showed the new estimator performed more efficiently than the MLE, Poisson Ridge Regression Estimator (PRE), Poisson Liu Estimator (PLE) and the Poisson KL (PKL) estimators. The real-life application also agreed with the simulation result. Conclusions: In general, the new estimator performed more efficiently than the MLE, PRE, PLE and the PKL when multicollinearity was present.

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21

Aladeitan, Benedicta B., Olukayode Adebimpe, Adewale F. Lukman, Olajumoke Oludoun, and Oluwakemi E. Abiodun. "Modified Kibria-Lukman (MKL) estimator for the Poisson Regression Model: application and simulation." F1000Research 10 (July 8, 2021): 548. http://dx.doi.org/10.12688/f1000research.53987.1.

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Background: Multicollinearity greatly affects the Maximum Likelihood Estimator (MLE) efficiency in both the linear regression model and the generalized linear model. Alternative estimators to the MLE include the ridge estimator, the Liu estimator and the Kibria-Lukman (KL) estimator, though literature shows that the KL estimator is preferred. Therefore, this study sought to modify the KL estimator to mitigate the Poisson Regression Model with multicollinearity. Methods: A simulation study and a real-life study were carried out and the performance of the new estimator was compared with some of the existing estimators. Results: The simulation result showed the new estimator performed more efficiently than the MLE, Poisson Ridge Regression Estimator (PRE), Poisson Liu Estimator (PLE) and the Poisson KL (PKL) estimators. The real-life application also agreed with the simulation result. Conclusions: In general, the new estimator performed more efficiently than the MLE, PRE, PLE and the PKL when multicollinearity was present.

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Hu, Yi, Xiaohua Xia, Ying Deng, and Dongmei Guo. "Higher Order Mean Squared Error of Generalized Method of Moments Estimators for Nonlinear Models." Discrete Dynamics in Nature and Society 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/324904.

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Generalized method of moments (GMM) has been widely applied for estimation of nonlinear models in economics and finance. Although generalized method of moments has good asymptotic properties under fairly moderate regularity conditions, its finite sample performance is not very well. In order to improve the finite sample performance of generalized method of moments estimators, this paper studies higher-order mean squared error of two-step efficient generalized method of moments estimators for nonlinear models. Specially, we consider a general nonlinear regression model with endogeneity and derive the higher-order asymptotic mean square error for two-step efficient generalized method of moments estimator for this model using iterative techniques and higher-order asymptotic theories. Our theoretical results allow the number of moments to grow with sample size, and are suitable for general moment restriction models, which contains conditional moment restriction models as special cases. The higher-order mean square error can be used to compare different estimators and to construct the selection criteria for improving estimator’s finite sample performance.

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23

Sherman, Robert P. "U-Processes in the Analysis of a Generalized Semiparametric Regression Estimator." Econometric Theory 10, no. 2 (June 1994): 372–95. http://dx.doi.org/10.1017/s0266466600008458.

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We prove -consistency and asymptotic normality of a generalized semiparametric regression estimator that includes as special cases Ichimura's semiparametric least-squares estimator for single index models, and the estimator of Klein and Spady for the binary choice regression model. Two function expansions reveal a type of U-process structure in the criterion function; then new U-process maximal inequalities are applied to establish the requisite stochastic equicontinuity condition. This method of proof avoids much of the technical detail required by more traditional methods of analysis. The general framework suggests other -consistent and asymptotically normal estimators.

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24

Delgado, Miguel A. "Semiparametric Generalized Least Squares in the Multivariate Nonlinear Regression Model." Econometric Theory 8, no. 2 (June 1992): 203–22. http://dx.doi.org/10.1017/s0266466600012767.

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Asymptotically efficient estimates for the multiple equations nonlinear regression model are obtained in the presence of heteroskedasticity of unknown form. The proposed estimator is a generalized least squares based on nonparametric nearest neighbor estimates of the conditional variance matrices. Some Monte Carlo experiments are reported.

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25

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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26

Zhao, Quanshui. "ASYMPTOTICALLY EFFICIENT MEDIAN REGRESSION IN THE PRESENCE OF HETEROSKEDASTICITY OF UNKNOWN FORM." Econometric Theory 17, no. 4 (July 27, 2001): 765–84. http://dx.doi.org/10.1017/s0266466601174050.

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We consider a linear model with heteroskedasticity of unknown form. Using Stone's (1977, Annals of Statistics 5, 595–645) k nearest neighbors (k-NN) estimation approach, the optimal weightings for efficient least absolute deviation regression are estimated consistently using residuals from preliminary estimation. The reweighted least absolute deviation or median regression estimator with the estimated weights is shown to be equivalent to the estimator using the true but unknown weights under mild conditions. Asymptotic normality of the estimators is also established. In the finite sample case, the proposed estimators are found to outperform the generalized least squares method of Robinson (1987, Econometrica 55, 875–891) and the one-step estimator of Newey and Powell (1990, Econometric Theory 6, 295–317) based on a Monte Carlo simulation experiment.

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27

Kitamura, Yuichi, and Peter C. B. Phillips. "Efficient IV Estimation in Nonstationary Regression." Econometric Theory 11, no. 5 (October 1995): 1095–130. http://dx.doi.org/10.1017/s026646660000997x.

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A limit theory for instrumental variables (IV) estimation that allows for possibly nonstationary processes was developed in Kitamura and Phillips (1992, Fully Modified IV, GIVE, and GMM Estimation with Possibly Non-stationary Regressors and Instruments, mimeo, Yale University). This theory covers a case that is important for practitioners, where the nonstationarity of the regressors may not be of full rank, and shows that the fully modified (FM) regression procedure of Phillips and Hansen (1990) is still applicable. FM. versions of the generalized method of moments (GMM) estimator and the generalized instrumental variables estimator (GIVE) were also developed, and these estimators (FM-GMM and FM-GIVE) were designed specifically to take advantage of potential stationarity in the regressors (or unknown linear combinations of them). These estimators were shown to deliver efficiency gains over FM-IV in the estimation of the stationary components of a model.This paper provides an overview of the FM-IV, FM-GMM, and FM-GIVE procedures and investigates the small sample properties of these estimation procedures by simulations. We compare the following five estimation methods: ordinary least squares, crude (conventional) IV, FM-IV, FM-GMM, and FM-GIVE. Our findings are as follows, (i) In terms of overall performance in both stationary and nonstationary cases, FM-IV is more concentrated and better centered than OLS and crude IV, though it has a higher root mean square error than crude IV due to occasional outliers, (ii) Among FM-IV, FM-GMM, and FM-GIVE, (a) when applied to the stationary coefficients, FM-GIVE generally outperforms FM-IV and FM-GMM by a wide margin, whereas the difference between the latter two is quite small when the AR roots of the stationary processes are rather large; and (b) when applied to the nonstationary coefficients, the three estimators are numerically very close. The performance of the FM-GIVE estimator is generally very encouraging.

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28

Chaturvedi, Anoop, Hikaru Hasegawa, Ajit Chaturvedi, and Govind Shukla. "Confidence Sets for the Coefficients Vector of a Linear Regression Model with Nonspherical Disturbances." Econometric Theory 13, no. 3 (June 1997): 406–29. http://dx.doi.org/10.1017/s0266466600005879.

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In this present paper, considering a linear regression model with nonspherical disturbances, improved confidence sets for the regression coefficients vector are developed using the Stein rule estimators. We derive the large-sample approximations for the coverage probabilities and the expected volumes of the confidence sets based on the feasible generalized least-squares estimator and the Stein rule estimator and discuss their ranking.

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29

Zinde-Walsh, Victoria. "ASYMPTOTIC THEORY FOR SOME HIGH BREAKDOWN POINT ESTIMATORS." Econometric Theory 18, no. 5 (July 17, 2002): 1172–96. http://dx.doi.org/10.1017/s0266466602185070.

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High breakdown point estimators in regression are robust against gross contamination in the regressors and also in the errors; the least median of squares (LMS) estimator has the additional property of packing the majority of the sample most tightly around the estimated regression hyperplane in terms of absolute deviations of the residuals and thus is helpful in identifying outliers. Asymptotics for a class of high breakdown point smoothed LMS estimators are derived here under a variety of conditions that allow for time series applications; joint limit processes for several smoothed estimators are examined. The limit process for the LMS estimator is represented via a generalized Gaussian process that defines the generalized derivative of the Wiener process.

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30

Yasin, Ahad, Muhammad Amin, Muhammad Qasim, Abdisalam Hassan Muse, and Adam Braima Soliman. "More on the Ridge Parameter Estimators for the Gamma Ridge Regression Model: Simulation and Applications." Mathematical Problems in Engineering 2022 (May 6, 2022): 1–18. http://dx.doi.org/10.1155/2022/6769421.

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The Gamma ridge regression estimator (GRRE) is commonly used to solve the problem of multicollinearity, when the response variable follows the gamma distribution. Estimation of the ridge parameter estimator is an important issue in the GRRE as well as for other models. Numerous ridge parameter estimators are proposed for the linear and other regression models. So, in this study, we generalized these estimators for the Gamma ridge regression model. A Monte Carlo simulation study and two real-life applications are carried out to evaluate the performance of the proposed ridge regression estimators and then compared with the maximum likelihood method and some existing ridge regression estimators. Based on the simulation study and real-life applications results, we suggest some better choices of the ridge regression estimators for practitioners by applying the Gamma regression model with correlated explanatory variables.

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31

KISETA, Jacques SABITI, Roger AKUMOSO LIENDI, Patrick KALEBA KABAMBI, Jean-Claude KAYEMBE, and Olivier MUTOMBO TSHINGOMBE. "Recursive and Non-Recursive Generalized Least-Squares Methods for Estimation of Time Series Models with Exogenous Variables." Engineering & Technology Review 3, no. 1 (February 11, 2022): 1–14. http://dx.doi.org/10.47285/etr.v3i1.111.

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We present in this paper two generalized least-squares (GLS) methods for estimating regression coefficients of time series models with exogenous variables. The non-recursive GLS method is a generalization of the GLS method suggested by Cochrane and Orcutt (1949). The proposed GLS method consists of a sequence of four linear regressions. A first regression is fitted and provides residuals. These residuals are modeled as an autoregressive process and are used in a second regression (or autoregression) for obtaining estimators of autoregressive coefficients. These estimators are used to generate transformed endogenous and exogenous variables. A third regression makes use of the lagged values of these transformed variables to estimate the regression coefficients. The estimators of the regression coefficients are used to determine the true residuals which are modeled as an ARMA process which is finally used for obtaining the estimators of autoregressive and moving average parameters. The second GLS method is a recursive version of the first GLS method where the estimators are updated at each time point on receipt of the additional observations. The Simulation results based on different model structures with varying numbers of observations are used to compare the performance of our methods with that of exact maximum likelihood (EML) estimates.

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32

Teng, Guangqiang, Boping Tian, Yuanyuan Zhang, and Sheng Fu. "Asymptotics of Subsampling for Generalized Linear Regression Models under Unbounded Design." Entropy 25, no. 1 (December 31, 2022): 84. http://dx.doi.org/10.3390/e25010084.

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The optimal subsampling is an statistical methodology for generalized linear models (GLMs) to make inference quickly about parameter estimation in massive data regression. Existing literature only considers bounded covariates. In this paper, the asymptotic normality of the subsampling M-estimator based on the Fisher information matrix is obtained. Then, we study the asymptotic properties of subsampling estimators of unbounded GLMs with nonnatural links, including conditional asymptotic properties and unconditional asymptotic properties.

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33

Ali, Asad, Muhammad Moeen Butt, and Muhammad Zubair. "Generalized Chain Regression-cum-Chain Ratio Estimator for Population Mean under Stratified Extreme-cum-Median Ranked Set Sampling." Mathematical Problems in Engineering 2022 (January 4, 2022): 1–13. http://dx.doi.org/10.1155/2022/9556587.

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Estimation of population mean of study variable Y suffers loss of precision in the presence of high variation in the data set. The use of auxiliary information incorporated in construction of an estimator under ranked set sampling scheme results in efficient estimation of population mean. In this paper, we propose an efficient generalized chain regression-cum-chain ratio type estimator to estimate finite population mean of study variable under stratified extreme-cum-median ranked set sampling utilizing information on two auxiliary variables. Mean square error (MSE) of the proposed generalized estimator is derived up to first order of approximation. The applications of the proposed estimator under symmetrical and asymmetrical probability distributions are discussed using simulation study and real-life data set for comparisons of efficiency. It is concluded that the proposed generalized estimator performs efficiently as compared to some existing estimators. It is also observed that the efficiency of the proposed estimator is directly proportional to the correlations between the study variable and its auxiliary variables.

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34

Théberge, Alain. "Estimation when the Covariance Structure of the Variable of Interest is Positive Definite." Journal of Official Statistics 33, no. 1 (March 1, 2017): 275–99. http://dx.doi.org/10.1515/jos-2017-0014.

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Abstract Generalized regression (GREG) estimation uses a model that assumes that the values of the variable of interest are not correlated. An extension of the GREG estimator to the case where the vector of interest has a positive definite covariance structure is presented in this article. This extension can be translated to the calibration estimators. The key to this extension lies in a generalization of the Horvitz-Thompson estimator which, in some sense, also assumes that the values of the variable of interest are not correlated. The Godambe-Joshi lower bound is another result which assumes a model with no correlation. This is also generalized to a vector of interest with a positive definite covariance structure, and it is shown that the generalized calibration estimator asymptotically attains this generalized lower bound. Properties of the new estimators are given, and they are compared with the Horvitz-Thompson estimator and the usual calibration estimator. The new estimators are applied to the Canadian Reverse Record Check survey and to the problem of variance estimation.

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35

Kim, Kyoo il, and Amil Petrin. "A Generalized Non-Parametric Instrumental Variable-Control Function Approach to Estimation in Nonlinear Settings." Journal of Econometric Methods 11, no. 1 (January 1, 2022): 91–125. http://dx.doi.org/10.1515/jem-2021-0038.

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Abstract When the endogenous variables enter non-parametrically into the regression equation standard linear instrumental variables approaches fail. Two existing solutions are the non-parametric instrumental variables (NPIVs) estimators, which are based on a set of conditional moment restrictions (CMRs), and the control function (CF) estimators, which use conditional mean independence (CMI) restrictions. Our first contribution is to show that – similar to CMI – the CMR place shape restrictions on the conditional expectation of the error given the instruments and endogenous variables that are sufficient for identification, and we call our new estimator based on these restrictions the CMR-CF estimator. Our second contribution is to develop an estimator for non-linear and non-parametric settings that can combine both CMR and CMI restrictions, which cannot be done in either the NPIV nor the non-parametric CF setting. This new “Generalized CMR-CF” uses both CMR and CMI restrictions together by allowing the conditional expectation of the structural error to depend on both instruments and control variables. When sieves are used to approximate both the structural function and the CF our estimator reduces to a series of least squares regressions. Our Monte Carlos illustrate that our new estimator performs well across several economic settings.

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36

Mariati, Ni Putu Ayu Mirah, I. Nyoman Budiantara, and Vita Ratnasari. "Combination Estimation of Smoothing Spline and Fourier Series in Nonparametric Regression." Journal of Mathematics 2020 (July 1, 2020): 1–10. http://dx.doi.org/10.1155/2020/4712531.

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So far, most of the researchers developed one type of estimator in nonparametric regression. But in reality, in daily life, data with mixed patterns were often encountered, especially data patterns which partly changed at certain subintervals, and some others followed a recurring pattern in a certain trend. The estimator method used for the data pattern was a mixed estimator method of smoothing spline and Fourier series. This regression model was approached by the component smoothing spline and Fourier series. From this process, the mixed estimator was completed using two estimation stages. The first stage was the estimation with penalized least squares (PLS), and the second stage was the estimation with least squares (LS). Those estimators were then implemented using simulated data. The simulated data were gained by generating two different functions, namely, polynomial and trigonometric functions with the size of the sample being 100. The whole process was then repeated 50 times. The experiment of the two functions was modeled using a mixture of the smoothing spline and Fourier series estimators with various smoothing and oscillation parameters. The generalized cross validation (GCV) minimum was selected as the best model. The simulation results showed that the mixed estimators gave a minimum (GCV) value of 11.98. From the minimum GCV results, it was obtained that the mean square error (MSE) was 0.71 and R2 was 99.48%. So, the results obtained indicated that the model was good for a mixture estimator of smoothing spline and Fourier series.

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37

Hussein, Saja Mohammad. "Comparison of Some Suggested Estimators Based on Differencing Technique in the Partial Linear Model Using Simulation." Baghdad Science Journal 16, no. 4 (December 1, 2019): 0918. http://dx.doi.org/10.21123/bsj.2019.16.4.0918.

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In this paper new methods were presented based on technique of differences which is the difference- based modified jackknifed generalized ridge regression estimator(DMJGR) and difference-based generalized jackknifed ridge regression estimator(DGJR), in estimating the parameters of linear part of the partially linear model. As for the nonlinear part represented by the nonparametric function, it was estimated using Nadaraya Watson smoother. The partially linear model was compared using these proposed methods with other estimators based on differencing technique through the MSE comparison criterion in simulation study.

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38

Özbay, Nimet, Selahattin Kaçıranlar, and Issam Dawoud. "The feasible generalized restricted ridge regression estimator." Journal of Statistical Computation and Simulation 87, no. 4 (August 29, 2016): 753–65. http://dx.doi.org/10.1080/00949655.2016.1224880.

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39

Ali, M. A., and A. A. Smadi. "Modified Generalized Stein Estimator of Regression Coefficients." Journal of Information and Optimization Sciences 13, no. 2 (May 1992): 303–9. http://dx.doi.org/10.1080/02522667.1992.10699114.

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40

Alheety, M. I., and B. M. Golam Kibria. "A Generalized Stochastic Restricted Ridge Regression Estimator." Communications in Statistics - Theory and Methods 43, no. 20 (September 30, 2014): 4415–27. http://dx.doi.org/10.1080/03610926.2012.724506.

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41

Cheng, Chi-Lun, and John W. Van Ness. "Generalized $M$-Estimators for Errors-in-Variables Regression." Annals of Statistics 20, no. 1 (March 1992): 385–97. http://dx.doi.org/10.1214/aos/1176348528.

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42

Bhat, Sharada V., and Bhargavi Deshpande. "A Generalized Class of Varying Kernel Regression Estimators." International Journal of Computational & Theoretical Statistics 06, no. 02 (November 1, 2019): 156–63. http://dx.doi.org/10.12785/ijcts/060205.

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43

Cox, Dennis D., and Finbarr O'Sullivan. "Penalized Likelihood-type Estimators for Generalized Nonparametric Regression." Journal of Multivariate Analysis 56, no. 2 (February 1996): 185–206. http://dx.doi.org/10.1006/jmva.1996.0010.

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44

Cho, MoonJung, John L. Eltinge, Julie Gershunskaya, and Larry Huff. "Evaluation of Generalized Variance Functions in the Analysis of Complex Survey Data." Journal of Official Statistics 30, no. 1 (March 1, 2014): 63–90. http://dx.doi.org/10.2478/jos-2014-0004.

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Abstract Two sets of diagnostics are presented to evaluate the properties of generalized variance functions (GVFs) for a given sample survey. The first set uses test statistics for the coefficients of multiple regression forms of GVF models. The second set uses smoothed estimators of the mean squared error (MSE) of GVF-based variance estimators. The smooth version of the MSE estimator can provide a useful measure of the performance of a GVF estimator, relative to the variance of a standard design-based variance estimator. Some of the proposed methods are applied to sample data from the Current Employment Statistics survey.

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45

Arashi, M., M. Roozbeh, N. A. Hamzah, and M. Gasparini. "Ridge regression and its applications in genetic studies." PLOS ONE 16, no. 4 (April 8, 2021): e0245376. http://dx.doi.org/10.1371/journal.pone.0245376.

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With the advancement of technology, analysis of large-scale data of gene expression is feasible and has become very popular in the era of machine learning. This paper develops an improved ridge approach for the genome regression modeling. When multicollinearity exists in the data set with outliers, we consider a robust ridge estimator, namely the rank ridge regression estimator, for parameter estimation and prediction. On the other hand, the efficiency of the rank ridge regression estimator is highly dependent on the ridge parameter. In general, it is difficult to provide a satisfactory answer about the selection for the ridge parameter. Because of the good properties of generalized cross validation (GCV) and its simplicity, we use it to choose the optimum value of the ridge parameter. The GCV function creates a balance between the precision of the estimators and the bias caused by the ridge estimation. It behaves like an improved estimator of risk and can be used when the number of explanatory variables is larger than the sample size in high-dimensional problems. Finally, some numerical illustrations are given to support our findings.

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46

Vishwakarma, Gajendra Kumar, and Sayed Mohammed Zeeshan. "Generalized Ratio-cum-Product Estimator for Finite Population Mean under Two-Phase Sampling Scheme." Journal of Modern Applied Statistical Methods 19, no. 1 (June 8, 2021): 2–16. http://dx.doi.org/10.22237/jmasm/1608553320.

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A method to lower the MSE of a proposed estimator relative to the MSE of the linear regression estimator under two-phase sampling scheme is developed. Estimators are developed to estimate the mean of the variate under study with the help of auxiliary variate (which are unknown but it can be accessed conveniently and economically). The mean square errors equations are obtained for the proposed estimators. In addition, optimal sample sizes are obtained under the given cost function. The comparison study has been done to set up conditions for which developed estimators are more effective than other estimators with novelty. The empirical study is also performed to supplement the claim that the developed estimators are more efficient.

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47

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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48

Mahaboob, B., B. Venkateswarlu, J. Ravi Sankar, J. Peter Praveen, and C. Narayana. "A Discourse on the Estimation of Nonlinear Regression Model." International Journal of Engineering & Technology 7, no. 4.10 (October 2, 2018): 992. http://dx.doi.org/10.14419/ijet.v7i4.10.26642.

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The present study evaluates an estimation for regression model which are nonlinear with Goldfeld, Quandt and exponential structure for heteroscedastic errors. An IENLGLS (Iterative Estimated Nonlinear Generalised Least Squares) estimator based on Goldfeld and Quandt for parametric vector has been derived in this research article. Volkan Soner Ozsoy e.t.al [1], in their paper, proposed an effective approach based on the particle Swarm Optimisation (PSO) algorithm in order to enhance the accuracy in the estimation of parameters of nonlinear regression model. Ting Zhang et.al [2], in their article, established an asymptotic theory for estimates of the time-varying regression functions. Felix Chan et.al [3], in their paper, proposed some principals which are sufficient for asymptotic normality and consistency of the MLH estimator

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49

Affleck, David L. R., and Timothy G. Gregoire. "Generalized and synthetic regression estimators for randomized branch sampling." Forestry 88, no. 5 (July 20, 2015): 599–611. http://dx.doi.org/10.1093/forestry/cpv027.

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50

Ohtani, K. "Generalized ridge regression estimators under the LINEX loss function." Statistical Papers 36, no. 1 (December 1995): 99–110. http://dx.doi.org/10.1007/bf02926024.

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