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Nonparametric and Varying Coefficient Modal Regression

In this article, we propose a new nonparametric data analysis tool, which we call nonparametric modal regression, to investigate the relationship among interested variables based on estimating the mode of the conditional density of a response variable Y given predictors X. The nonparametric modal regression is distinguished from the conventional nonparametric regression in that, instead of the conditional average or median, it uses the "most likely" conditional values to measures the center. Better prediction performance and robustness are two important characteristics of nonparametric modal regression compared to traditional nonparametric mean regression and nonparametric median regression. We propose to use local polynomial regression to estimate the nonparametric modal regression. The asymptotic properties of the resulting estimator are investigated. To broaden the applicability of the nonparametric modal regression to high dimensional data or functional/longitudinal data, we further develop a nonparametric varying coefficient modal regression. A Monte Carlo simulation study and an analysis of health care expenditure data demonstrate some superior performance of the proposed nonparametric modal regression model to the traditional nonparametric mean regression and nonparametric median regression in terms of the prediction performance.