Nonparametric modal regression
This work addresses modal regression for statistical analysis, offering a method to reveal structure missed by mean-based regression, but it appears incremental as it builds on existing kernel density estimation techniques.
The paper tackles the problem of estimating local modes of the conditional distribution in regression, rather than the mean, using a nonparametric method based on kernel density estimation, and derives asymptotic error bounds and techniques for confidence and prediction sets.
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.