Nonparametric modal regression

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.

Published at http://dx.doi.org/10.1214/15-AOS1373 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• Generalized Mode and Ridge Estimation

Cited by in corpus (22)

• A Statistical Learning Approach to Modal Regression
• Tensor Methods for Additive Index Models under Discordance and Heterogeneity
• Optimal Ridge Detection using Coverage Risk
• Nonparametric multimodal regression for circular data
• Importance Sampling and its Optimality for Stochastic Simulation Models
• Bayesian Modal Regression based on Mixture Distributions
• Quantile regression approach to conditional mode estimation
• Density Level Sets: Asymptotics, Inference, and Visualization
• An implicit function learning approach for parametric modal regression
• Multivariate Smoothing via the Fourier Integral Theorem and Fourier Kernel
• PATHFINDER: Designing Stimuli for Neuromodulation through data-driven inverse estimation of non-linear functions
• Bump hunting through density curvature features
• Parametric Modal Regression with Error in Covariates
• Bandwidth selection for nonparametric modal regression
• Nonparametric modal regression in the presence of measurement error
• Uniform Consistency in Nonparametric Mixture Models
• On Estimation of Conditional Modes Using Multiple Quantile Regressions
• The Mode Treatment Effect
• Robust modal regression with direct log-density derivative estimation
• Space Partitioning and Regression Mode Seeking via a Mean-Shift-Inspired Algorithm
• Nonlinear Modal Interval Regression for Bivariate Data Analysis
• Parametric mode regression for bounded responses