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Publication Citation: Model Selection for Good Estimation and Prediction Over a User-Speci ed Covariate Distribution for Linear Models Under the Frequentist Paradigm

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Author(s): Adam L. Pintar;
Title: Model Selection for Good Estimation and Prediction Over a User-Speci ed Covariate Distribution for Linear Models Under the Frequentist Paradigm
Published: October 26, 2011
Abstract: Model selection is an important part of estimation and prediction for linear models with multiple explanatory variables (covariates). A variety of approaches exist that focus on estimation of model parameters or the t of the model where data have been observed. This article proposes an alternative strategy that selects models based on mean squared error of the estimated expected response for a user-speci ed distribution of interest on the covariate space. We discuss numerical and graphical tools for detailed comparisons among di erent models. These tools help select a best model based on its ability to estimate the mean response over covariate locations likely to arise from a distribution of interest, and can be combined with cost for deciding whether to include speci c covariates. The new method is illustrated with three examples. We also present simulation results demonstrating situations where the new method shows improvement over some standard alternatives.
Citation: Quality and Reliability Engineering International
Keywords: Akaike information criterion; Correlated variables; Cross validation; Fraction of design space; Mean squared error.
Research Areas: Statistics