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A class of generalized shrunken least squares estimators in linear model

Modern data analysis often involves a large number of variables, which gives rise to the problem of multicollinearity in regression models. It is well-known that in a linear model, when the design matrix X is nearly singular, then the ordinary least squares (OLS) estimator may perform poorly because of its numerical instability and large variance. To overcome this problem, many linear or nonlinear biased estimators are studied. In this work we consider a class of generalized shrunken least squares (GSLS) estimators that include many well-known linear biased estimators proposed in the literature. We compare these estimators under the mean square error and matrix mean square error criteria. Moreover, a simulation study and two numerical examples are used to illustrate some of the theoretical results.

Identiferoai:union.ndltd.org:MANITOBA/oai:mspace.lib.umanitoba.ca:1993/4188
Date13 September 2010
CreatorsLiu, Xiaoming
ContributorsWang, Liqun (Statistics), Mandal, Saumen (Statistics) Zhang, Yang (Mathematics)
Source SetsUniversity of Manitoba Canada
Languageen_US
Detected LanguageEnglish

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