Comparison of Some Estimators under the Pitman’s Closeness Criterion in Linear Regression Model

Jibo Wu

Type: Article

Publication Date: 2014-01-01

Citations: 3

DOI: https://doi.org/10.1155/2014/654949

Abstract

Batah et al. (2009) combined the unbiased ridge estimator and principal components regression estimator and introduced the modified<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>r</mml:mi><mml:mtext>-</mml:mtext><mml:mi>k</mml:mi></mml:math>class estimator. They also showed that the modified<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>r</mml:mi><mml:mtext>-</mml:mtext><mml:mi>k</mml:mi></mml:math>class estimator is superior to the ordinary least squares estimator and principal components regression estimator in the mean squared error matrix. In this paper, firstly, we will give a new method to obtain the modified<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mi>r</mml:mi><mml:mtext>-</mml:mtext><mml:mi>k</mml:mi></mml:math>class estimator; secondly, we will discuss its properties in some detail, comparing the modified<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mi>r</mml:mi><mml:mtext>-</mml:mtext><mml:mi>k</mml:mi></mml:math>class estimator to the ordinary least squares estimator and principal components regression estimator under the Pitman closeness criterion. A numerical example and a simulation study are given to illustrate our findings.

Locations

Journal of Applied Mathematics - View - PDF
Project Euclid (Cornell University) - View - PDF
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Works Cited by This (18)

Action	Title	Year	Authors
+	The “closest” estimates of statistical parameters	1937	E. J. G. Pitman
+	Comparison of regression estimators using Pitman measures of nearness	2001	Eshetu Wencheko
+	Mean Squared Error Matrix Comparisons of Some Biased Estimators in Linear Regression	2003	Fikri Akdeniz Hamza Erol
+	Using Liu-Type Estimator to Combat Collinearity	2003	Kejian Liu
+	Pitman closeness of current records for location-scale families	2010	Jafar Ahmadi N. Balakrishnan
+	Combining Unbiased Ridge and Principal Component Regression Estimators	2009	Feras Sh. M. Batah M. Revan Özkale Sharad D. Gore
+	Two Stochastic Restricted Principal Components Regression Estimator in Linear Regression	2013	Jibo Wu Hu Yang
+	Ridge Regression: Biased Estimation for Nonorthogonal Problems	2000	Arthur E. Hoerl Robert W. Kennard
+	The Restricted and Unrestricted Two-Parameter Estimators	2007	M. Revan Özkale Selahattin Kaçıranlar
+	Unbiased ridge estimation with prior information and ridge trace	1995	Robert H. Crouse Chun Jin R. Choudary Hanumara