Mean Squared Error Matrix comparison of Least Squares and Stein-Rule Estimators for Regression Coefficients under Non-normal Disturbances
نویسنده
چکیده
Choosing the performance criterion to be mean squared error matrix, we have compared the least squares and Stein-rule estimators for coefficients in a linear regression model when the disturbances are not necessarily normally distributed. It is shown that none of the two estimators dominates the other, except in the trivial case of merely one regression coefficient where least squares is found to be superior in comparisons to Stein-rule estimators.
منابع مشابه
Confidence ellipsoids based on a general family of shrinkage estimators for a linear model with non-spherical disturbances
Confidence ellipsoids based on a general family of shrinkage estimators for a linear model with non-spherical disturbances, This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is pu...
متن کاملRisk Performance Of Stein-Rule Estimators Over The Least Squares Estimators Of Regression Coefficients Under Quadratic Loss Structures
This paper presents a general loss function under quadratic loss structure and discusses the comparison of risk functions associated with the unbiased least squares and biased Stein-rule estimators of the coefficients in a linear regression model. ∗Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur 208016, India. E-mail: [email protected], [email protected] (Corre...
متن کاملWeaker Mse Criteria and Tests for Linear Restrictions in Regression Models with Non-spherical Disturbances
This paper extends, in an asymptotic sense, the strong and the weaker mean square error criteria and corresponding tests to linear models with non-spherical disturbances where the error covariance matrix is unknown but a consistent estimator for it is available. The mean square error tests of Toro-Vizcorrondo and Wallace (1968) and Wallace (1972) test for the superiority of restricted over unre...
متن کاملRobust Estimation of Multiple Regression Model with Non-normal Error: Symmetric Distribution
In this paper, we develop the modified maximum likelihood (MML) estimators for the multiple regression coefficients in linear model with the underlying distribution assumed to be symmetric, one of Student's t family. We obtain the closed form of the estimators and derive their asymptotic properties. In addition, we demonstrate that the MML estimators are more appropriate to estimate the paramet...
متن کاملComparison of Small Area Estimation Methods for Estimating Unemployment Rate
Extended Abstract. In recent years, needs for small area estimations have been greatly increased for large surveys particularly household surveys in Sta­ tistical Centre of Iran (SCI), because of the costs and respondent burden. The lack of suitable auxiliary variables between two decennial housing and popula­ tion census is a challenge for SCI in using these methods. In general, the...
متن کامل