Model Selection in Regression Based on Presmoothing

Abstract

In this paper we investigate the effect of presmoothing on model selection. ChristobalChristobal et al. (1987) showed the beneficial effect of presmoothing for estimating the parameters in a linear regression model. Here, in a regression setting, we show that smoothing the response data prior to model selection by Akaike's Information Criterion can lead to an improved selection procedure. The bootstrap is used tocontrol the magnitude of the random error structure in the smoothed data. Theeffect of presmoothing on model selection is shown in simulations. The method is illustrated in a variety of settings, including the selection of the best fractional polynomial in a generalized linear model.

Keywords: Akaike Information Criterion, Fractional Polynomial, Latent Variable Model, Model Selection, Presmoothing