Improved Estimators Under Squared Error Loss (Stein Estimator, Decision Theory, Empirical Bayes, Quadratic, Robust Estimation)
Miyazaki, Shigetaka
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https://hdl.handle.net/2142/70766
Description
Title
Improved Estimators Under Squared Error Loss (Stein Estimator, Decision Theory, Empirical Bayes, Quadratic, Robust Estimation)
Author(s)
Miyazaki, Shigetaka
Issue Date
1985
Department of Study
Economics
Discipline
Economics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Statistics
Abstract
Much work on the James-Stein (1964) estimator or an improved estimator under squared error loss has been done with the assumption of independently identically distributed normal errors.
In this thesis behavior of the Stein-type estimators is examined in a regression model under the assumptions of heteroscedasticity and non-normality. Also presented are relationship between the Bayes and the Stein-type estimators, improved estimators under inequality prior restrictions, impacts of pre-testing null hypotheses in estimating parameters, and compromise estimators between the minimum maximum component risk and the minimum ensemble risk. Monte Carlo experiments are done as well as theoretical work on these improved estimators. It is then shown that even under the assumptions of heteroscedasticity and non-normality the Stein-type estimators are still risk superior to the maximum likelihood estimator and conventional robust estimators everywhere on the parameter space. Also, the adaptive Stein estimator introduced by Dey-Berger (1983, JASA) is shown to be risk superior to the conventional Stein estimator under some circumstances.
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