Nonparametric Modal Regression

• Activity Number: 74
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yen-Chi Chen* and Christopher R. Genovese and Ryan Joseph Tibshirani and Larry Wasserman
• Companies: Carnegie Mellon University and Carnegie Mellon University and Carnegie Mellon University and Carnegie Mellon University
• Keywords: nonparametric regression ; modes ; mixture model ; confidence set ; prediction set ; bootstrap

Abstract

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.