Comparison of Two Estimators of Parameters Under Pitman Nearness Criterion

In this article, Pitman nearness criterion is used to compare two competing united biased estimators in linear model. In particular, a sufficient and necessary condition for one estimator being superior to the other is derived. Furthermore, a simulation study is performed to illustrate the theoretical results and several special cases are also studied.     

Linearized Ridge Regression Estimator Under the Mean Squared Error Criterion in a Linear Regression Model

This article mainly aims to study the superiority of the notion of linearized ridge regression estimator (LRRE) under the mean squared error criterion in a linear regression model. Firstly, we derive uniform lower bound of MSE for the class of the generalized shrinkage estimator (GSE), based on which it is shown that the optimal LRRE is the best estimator in the class of GSE's. Secondly, we propose the notion of the almost unbiased completeness and show that LRRE possesses such a property. Thirdly, the simulation study is given, from which it indicates that the LRRE performs desirably. Finally, the main results are applied to the well known Hald data.     

Risk Comparison of Inequality Constrained Estimators in the Heteroscedastic Linear Model

There exist many studies which treat the inequality and/or interval constraints on coefficients in the homoscedastic linear regression model. However, the sampling performance of the inequality constrained estimators in the heteroscedastic linear model has not been examined. This paper considers the inequality constrained estimators in the heteroscedastic linear regression model and derives their risks under a quadratic loss function. Furthermore, using the inequality constrained estimators, we introduce a pre-test estimator which might be employed after the test for homoscedasticity and derive its risk. In addition, the risk performance of these estimators is evaluated numerically.     

Isotonic Window Estimators of the Baseline Hazard Function in Cox's Regression Model Under Order Restriction

The regression model suggested by Cox (1972) has been widely used in survival analysis with censored observations. We propose isotonic window estimators for a monotone baseline hazard function in the Cox regression model. We prove that these estimators are asymptotically normal. The simulati on results presented in the article suggest that the proposed estimator performs better than several existing estimators in the literature     

Monte Carlo Simulation Study of Biased Estimators in the Linear Regression Models with Correlated or Heteroscedastic Errors

In this study, the performance of the estimators proposed in the presence of multicollinearity in the linear regression model with heteroscedastic or correlated or both error terms is investigated under the matrix mean square error criterion. Structures of the autocorrelated error terms are given and a Monte Carlo simulation study is conducted to examine the relative efficiency of the estimators against each other.     

Performances of the Positive-Rule Stein-Type Ridge Estimator in a Linear Regression Model with Spherically Symmetric Error Distributions

In this article, the positive-rule Stein-type ridge estimator (PSRE) is introduced for the parameters in a multiple linear regression model with spherically symmetric error distributions when it is suspected that the parameter vector may be restricted to a linear manifold. The bias and quadratic risk functions of the PSRE are derived and compared with some related competing estimators in literatures. Particularly, some sufficient conditions are derived for superiority of the PSRE over the ordinary ridge estimator, the restricted ridge estimator and the preliminary test ridge estimator, respectively. Furthermore, some graphical results are provided to illustrate some of the theoretical results.     

On Small Sample Properties of the Wald,LR and LM Tests in a Linear Model with AR(1) Errors

When the error terms are autocorrelated, the conventional t-tests for individual regression coefficients mislead us to over-rejection of the null hypothesis. We examine, by Monte Carlo experiments, the small sample properties of the unrestricted estimator of ρ and of the estimator of ρ restricted by the null hypothesis. We compare the small sample properties of the Wald, likelihood ratio and Lagrange multiplier test statistics for individual regression coefficients. It is shown that when the null hypothesis is true, the unrestricted estimator of ρ is biased. It is also shown that the Lagrange multiplier test using the maximum likelihood estimator of ρ performs better than the Wald and likelihood ratio tests.     

Empirical Bayes Estimation of Small Area Means under a Nested Error Linear Regression Model with Measurement Errors in the Covariates

Abstract.  Previously, small area estimation under a nested error linear regression model was studied with area level covariates subject to measurement error. However, the information on observed covariates was not used in finding the Bayes predictor of a small area mean. In this paper, we first derive the fully efficient Bayes predictor by utilizing all the available data. We then estimate the regression and variance component parameters in the model to get an empirical Bayes (EB) predictor and show that the EB predictor is asymptotically optimal. In addition, we employ the jackknife method to obtain an estimator of mean squared prediction error (MSPE) of the EB predictor. Finally, we report the results of a simulation study on the performance of our EB predictor and associated jackknife MSPE estimators. Our results show that the proposed EB predictor can lead to significant gain in efficiency over the previously proposed EB predictor.