Quantile regression approach to conditional mode estimation

TL;DR

This paper introduces a scalable quantile regression-based estimator for the conditional mode, providing asymptotic theory, confidence intervals, and empirical validation through simulations and real data application.

Contribution

It develops a novel estimator for the conditional mode using quantile regression, with theoretical properties and practical confidence interval methods.

Findings

Asymptotic distribution is a scaled Chernoff's distribution.

Estimator performs well in finite samples according to simulations.

Application to power plant data demonstrates practical utility.

Abstract

In this paper, we consider estimation of the conditional mode of an outcome variable given regressors. To this end, we propose and analyze a computationally scalable estimator derived from a linear quantile regression model and develop asymptotic distributional theory for the estimator. Specifically, we find that the pointwise limiting distribution is a scale transformation of Chernoff's distribution despite the presence of regressors. In addition, we consider analytical and subsampling-based confidence intervals for the proposed estimator. We also conduct Monte Carlo simulations to assess the finite sample performance of the proposed estimator together with the analytical and subsampling confidence intervals. Finally, we apply the proposed estimator to predicting the net hourly electrical energy output using Combined Cycle Power Plant Data.