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

Published

Author(s)

Adam L. Pintar

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.

Citation

Pintar, A. (2011), Model Selection for Good Estimation and Prediction Over a User-Speci ed Covariate Distribution for Linear Models Under the Frequentist Paradigm, Quality and Reliability Engineering International (Accessed June 14, 2024)

Issues

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Created October 26, 2011, Updated January 27, 2020