  Modal regression estimates the local modes of the distribution of $Y$ given
$X=x$, instead of the mean, as in the usual regression sense, and can hence
reveal important structure missed by usual regression methods. We study a
simple nonparametric method for modal regression, based on a kernel density
estimate (KDE) of the joint distribution of $Y$ and $X$. We derive asymptotic
error bounds for this method, and propose techniques for constructing
confidence sets and prediction sets. The latter is used to select the smoothing
bandwidth of the underlying KDE. The idea behind modal regression is connected
to many others, such as mixture regression and density ridge estimation, and we
discuss these ties as well.
