Robust regression modeling and predictive recursion maximum likelihood
Ryan Martin, Zhen Yu Han · arXiv (Cornell University) · 2013
AbstractIn a regression context, robustness to specification of the error distribution isimportant. In this paper, we propose a general nonparametric scale mixture modelfor the error distribution. For such mixtures, the predictive recursion method hasbeen shown to be a simple and computationally efficient alternative to existingmethods. Here, a predictive recursion-based likelihood function is constructed, andestimation of the regression parameters proceeds by maximizing this function. Ahybrid predictive recursion–EM algorithm is proposed for this purpose, and sim-ulations and real data analyses compare its performance to a variety of existingmethods. A useful by-product of the hybrid algorithm is a sequence of scores whichcan be used to identify outliers.Keywords and phrases: EM algorithm; Dirichlet process; marginal likelihood;nonparametric maximum likelihood; normal scale mixture; profile likelihood. 1 Introduction Consider the standard linear regression model,Y = Xβ+e,where Xis a n×pmatrix of covariates, βis a p×1 vector of regression coefficients, ande= (e