Chapter IO
BIASED ESTIMATION
G. G. JUDGE and M. E. BOCK*
University of Illinois and Purdue University
Contents
1. Introduction
2. Conventional statistical models, estimators, tests, and measures of
estimator performance
2.1. Conventional estimators and tests
2.2. Measures of performance
2.3. Bayes estimation
3. Some possibly biased alternatives
3.1. Exact non-sample information
3.2. Stochastic non-sample information
3.3. Inequality non-sample information
3.4. Parameter distribution information (prior)
3.5. Some remarks
4. Pre-test-variable selection estimators
4.1. Conventional equality pre-test estimator
4.2. Stochastic hypothesis pre-test estimator
4.3. Inequality hypothesis pre-test estimator
4.4. Bayesian pre-test estimators
4.5. Variable selection estimators
5. Conventional estimator inadmissibility and the Stein-rule alternatives
5.1. Estimation under squared error loss
5.2. Stein-like rules under weighted squared error loss
6. Some biased estimator alternatives for the stochastic regressor case
7. Biased estimation with nearly collinear data
7.1. A measure of “near” collinearity
7.2. Ridge-type estimators
7.3. Minimax ridge-type estimators 643
7.4. Generalized ridge estimators 644
7.5. A summary comment 645
8. Some final comments 645
References 647