Stein Estimation and Model Selection

104 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1986.This thesis attempts to use Stein type estimators for statistical model selection purposes. First, a parameter truncation criterion developed in conjunction with the new Stein estimator (Stein, 1981) is used in an orthonormal linear statistical model setting, as a basis for simultaneously selecting the model and estimating the unknown parameters. Using a mean squared error of prediction (MSEP) loss measure, the sampling performance of the extended Stein procedure (ESP) is analyzed for two alternative structures of the parameter space and under normal and non-normal errors. Second, the problem of simultaneously selecting the model and estimating the unknown parameters in a general linear model is considered. An estimator is proposed for this dual purposes which is essentially a Stein type estimator where the shrinkage occurs towards a restricted least squares estimator. The restrictions are model selection restrictions, and a choice between different restrictions is made by a generalized model selection criterion called generalized C(,P) criterion (GC(,P)). Minimizing the GC(,P) criterion with respect to the restrictions and the amount of shrinkage yields the model and its parameter estimates. The sampling performance of this shrinkage criterion is evaluated by Monte Carlo simulations.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD