Variable Selection for Heteroscedastic Data Through Variance Estimation

Abstract

ABSTRACT In this article, we extend some variable selection criteria in regression analysis to heteroscedastic models. First, a sequential test procedure is proposed to identify potential heteroscedasticity of the error variances. Next, we develop a variance estimation method to estimate the variance–covariance matrix for data with unequal variances. We improve Mallows’ C p and AIC using the proposed variance estimation method. This work is motivated by the poor behavior of C p in highly heteroscedastic models and by the fact that C p can be written as a linear function of an F statistic for testing the fit of a regression model. The proposed method performs well for both homoscedastic and heteroscedastic data. Simulation results show that our method is superior to C p for data with significant heteroscedasticity and is comparable in accuracy for homoscedastic models. The new method is illustrated with real data. Keywords: Akaike information criterionExperimental designHomoscedasticityMallows’ C p RegressionVariance estimationMathematics Subject Classification: 62J0562J15 Acknowledgment The authors would like to thank Kenny Ye for helpful discussions.