Nonparametric statistical learning based on modal regression
Sijia Xiang, Weixin Yao
Abstract
In this article, we propose a novel nonparametric statistical learning tool based on modal regression, which can complement the standard mean and quantile regression and has broad applicability in various fields. We first propose a local polynomial modal regression which focuses on the most likely conditional value (conditional mode) of a dependent variable Y given covariates x, and has several superiorities over conditional mean or quantiles, such as resistance to outliers and some forms of measurement error and having shorter prediction intervals when data are skewed. We employ the idea of local polynomial regression to estimate the modal regression nonparametrically. To broaden the applicability of the new technique to multivariate data or functional/longitudinal data, we further develop a varying coefficient modal regression. A Monte Carlo simulation study and an analysis of health care expenditure data demonstrate that the new proposed nonparametric modal regression is a promising complementary nonparametric data analysis tool to conventional nonparametric mean or quantile regression.