  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.
