A semiparametric scale-mixture regression model and predictive recursion maximum likelihood

TL;DR

This paper introduces a nonparametric scale mixture regression model that avoids specifying error distribution, utilizing a computationally efficient predictive recursion-based method for estimation, validated through simulations and real data.

Contribution

It develops a novel semiparametric regression approach using predictive recursion for error distribution estimation, offering a practical alternative to existing methods.

Findings

The proposed method performs well in simulations.

It effectively models error distributions without parametric assumptions.

Application to real data demonstrates its practical utility.

Abstract

To avoid specification of the error distribution in a regression model, we propose a general nonparametric scale mixture model for the error distribution. For fitting such mixtures, the predictive recursion method is a simple and computationally efficient alternative to existing methods. We define a predictive recursion-based marginal likelihood function, and estimation of the regression parameters proceeds by maximizing this function. A hybrid predictive recursion--EM algorithm is proposed for this purpose. The method's performance is compared with that of existing methods in simulations and real data analyses.