Group Variable Selection For Nonparametric Additive Beta Regression Models

The beta regression models are commonly used by practitioners to model the response variable that is restricted in the standard unit interval(0,1).In this paper,we extend the parametric beta regression model proposed by Ferrari and Cribari-Neto(2004)[1]to nonparametric additive beta regression model together with a variable selection procedure,where the mean response is related to covariates by means of the combination of unknown functions of covariates,which can be approximated by B-spline basis.With the help of this approximation,the problem of component selection becomes that of selecting the groups of coefficients in the expansion.Based on the penalized likelihood method for group variable selection,we successfully select out the zero components.The consistency and property of the penalized estimators are established.Simulation studies and real data analysis are presented to illustrate the usefulness of the proposed methods.