Difference-based variance estimator for nonparametric regression in complex surveys

A difference-based variance estimator is proposed for nonparametric regression in complex surveys. By using a combined inference framework, the estimator is shown to be asymptotically normal and to converge to the true variance at a parametric rate. Simulation studies show that the proposed variance estimator works well for complex survey data and also reveals some finite sample properties of the estimator.     

Improved Liu estimator in a linear regression model

In this paper, we mainly aim to introduce the notion of improved Liu estimator (ILE) in the linear regression model y=Xβ+e. The selection of the biasing parameters is investigated under the PRESS criterion and the optimal selection is successfully derived. We make a simulation study to show the performance of ILE compared to the ordinary least squares estimator and the Liu estimator. Finally, the main results are applied to the Hald data.     

Comment on a generalized stochastic restricted ridge regression estimator

In this note, we make some comments about the paper of Alheety and Kibria (2014 Alheety, M.I., Kibria, B.M.G. (2014). A generalized stochastic restricted ridge regression estimator. Commun. Stat. Theor. Meth. 43:4415–4427.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) and correct the wrongly proved Theorems in that paper.     

New difference-based estimator of parameters in semiparametric regression models

The paper introduces a new difference-based Liu estimator β?_Ldiff=([Xtilde]′[Xtilde]+I)^?1([Xtilde]′[ytilde]+η β?_diff) of the regression parameters β in the semiparametric regression model, y=Xβ+f+?. Difference-based estimator, β?_diff=([Xtilde]′[Xtilde])^?1[Xtilde]′[ytilde] and difference-based Liu estimator are analysed and compared with respect to mean-squared error (mse) criterion. Finally, the performance of the new estimator is evaluated for a real data set. Monte Carlo simulation is given to show the improvement in the scalar mse of the estimator.     

Asymptotic properties of a quast-maximum likelihood estimator in truncated regression model with serial correlation

Robinson (1982a) presented a general approach to serial correlation in limited dependent variable models and proved the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator (QMLE) for the Tobit model with serial correlation, obtained under the assumption of independent errors. This paper proves the strong consistency and asymptotic normality of the QMLE based on independent errors for the truncated regression model with serial correlation and gives consistent estimators for the limiting covariance matrix of the QMLE.     

Asymptotic properties of a quast-maximum likelihood estimator in truncated regression model with serial correlation

Robinson (1982a) presented a general approach to serial correlation in limited dependent variable models and proved the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator (QMLE) for the Tobit model with serial correlation, obtained under the assumption of independent errors. This paper proves the strong consistency and asymptotic normality of the QMLE based on independent errors for the truncated regression model with serial correlation and gives consistent estimators for the limiting covariance matrix of the QMLE.     

New generalized regression estimator in the presence of non response under unequal probability sampling

In this paper, we propose a new generalized regression estimator for the problem of estimating the population total using unequal probability sampling without replacement. A modified automated linearization approach is applied in order to transform the proposed estimator to estimate variance of population total. The variance and estimated value of the variance of the proposed estimator is investigated under a reverse framework assuming that the sampling fraction is negligible and there are equal response probabilities for all units. We prove that the proposed estimator is an asymptotically unbiased estimator and that it does not require a known or estimated response probability to function.     

A comparison of biased regression estimators using a pitman nearness criterion

Biased regression estimators have traditionally benn studied using the Mean Square Error (MSE) criterion. Usually these comparisons have been based on the sum of the MSE's of each of the individual parameters, i.e., a scaler valued measure that is the trace of the MSE matrix. However, since this summed MSE does not consider the covariance structure of the estimators, we propose the use of a Pitman Measure of Closeness (PMC) criterion (Keating and Gupta, 1984; Keating and Mason, 1985). In this paper we consider two versions of PMC. One of these compares the estimates and the other compares the resultant predicted values for 12 different regression estimators. These estimators represent three classes of estimators, namely, ridge, shrunken, and principal component estimators. The comparisons of these estimators using the PMC criteria are contrasted with the usual MSE criteria as well as the prediction mean square error. Included in the estimators is a relatively new estimator termed the generalized principal component estimator proposed by Jolliffe. This estimator has previously received little attention in the literature.     

Performance of ridge estimator in inverse Gaussian regression model

The presence of multicollinearity among the explanatory variables has undesirable effects on the maximum likelihood estimator (MLE). Ridge estimator (RE) is a widely used estimator in overcoming this issue. The RE enjoys the advantage that its mean squared error (MSE) is less than that of MLE. The inverse Gaussian regression (IGR) model is a well-known model in the application when the response variable positively skewed. The purpose of this paper is to derive the RE of the IGR under multicollinearity problem. In addition, the performance of this estimator is investigated under numerous methods for estimating the ridge parameter. Monte Carlo simulation results indicate that the suggested estimator performs better than the MLE estimator in terms of MSE. Furthermore, a real chemometrics dataset application is utilized and the results demonstrate the excellent performance of the suggested estimator when the multicollinearity is present in IGR model.     

Réduction de la variance dans les sondages en présence d'information auxiliarie: Une approache non paramétrique par splines de régression

The author considers the use of auxiliary information available at population level to improve the estimation of finite population totals. She introduces a new type of model‐assisted estimator based on nonparametric regression splines. The estimator is a weighted linear combination of the study variable with weights calibrated to the B‐splines known population totals. The author shows that the estimator is asymptotically design‐unbiased and consistent under conditions which do not require the superpopulation model to be correct. She proposes a design‐based variance approximation and shows that the anticipated variance is asymptotically equivalent to the Godambe‐Joshi lower bound. She also shows through simulations that the estimator has good properties.     

Properties of the mixed regression estimator when disturbances are not necessarily normal

Small-disturbance approximations for the bias vector and mean squared error matrix of the mixed regression estimator for the coefficients in a linear regression model are derived and efficiency with respect to least squares estimator is examined.     

Efficiency of the generalized difference-based Liu estimators in semiparametric regression models with correlated errors

In this paper, a generalized difference-based estimator is introduced for the vector parameter β in the semiparametric regression model when the errors are correlated. A generalized difference-based Liu estimator is defined for the vector parameter β in the semiparametric regression model. Under the linear nonstochastic constraint Rβ=r, the generalized restricted difference-based Liu estimator is given. The risk function for the β?_GRD(η) associated with weighted balanced loss function is presented. The performance of the proposed estimators is evaluated by a simulated data set.     

Finite sample properties of an HPT estimator when each individual regression coefficient is estimated in a misspecified linear regression model

ABSTRACT

In this paper, assuming that there exist omitted variables in the specified model, we analytically derive the exact formula for the mean squared error (MSE) of a heterogeneous pre-test (HPT) estimator whose components are the ordinary least squares (OLS) and feasible ridge regression (FRR) estimators. Since we cannot examine the MSE performance analytically, we execute numerical evaluations to investigate small sample properties of the HPT estimator, and compare the MSE performance of the HPT estimator with those of the FRR estimator and the usual OLS estimator. Our numerical results show that (1) the HPT estimator is more efficient when the model misspecification is severe; (2) the HPT estimator with the optimal critical value obtained under the correctly specified model can be safely used even when there exist omitted variables in the specified model.     

Performance of the almost unbiased ridge-type principal component estimator in logistic regression model

ABSTRACT

This article considers some different parameter estimation methods in logistic regression model. In order to overcome multicollinearity, the almost unbiased ridge-type principal component estimator is proposed. The scalar mean squared error of the proposed estimator is derived and its properties are investigated. Finally, a numerical example and a simulation study are presented to show the performance of the proposed estimator.     

A class of Stein‐rules in multivariate regression model with structural changes

In this paper, we consider an estimation problem of the matrix of the regression coefficients in multivariate regression models with unknown change‐points. More precisely, we consider the case where the target parameter satisfies an uncertain linear restriction. Under general conditions, we propose a class of estimators that includes as special cases shrinkage estimators (SEs) and both the unrestricted and restricted estimator. We also derive a more general condition for the SEs to dominate the unrestricted estimator. To this end, we extend some results underlying the multidimensional version of the mixingale central limit theorem as well as some important identities for deriving the risk function of SEs. Finally, we present some simulation studies that corroborate the theoretical findings.