Local Quantile Regression

TL;DR

This paper introduces an adaptive local quantile regression method that estimates conditional quantile curves flexibly, balancing bias and variance, with theoretical guarantees and practical applications in finance and climate risk analysis.

Contribution

It proposes a novel local model selection technique for quantile regression that adapts to data at each point, outperforming fixed global models.

Findings

The method performs comparably to an oracle estimator in simulations.

Applications demonstrate its effectiveness in financial tail dependence analysis.

The approach provides detailed insights into temperature risk factors.

Abstract

Quantile regression is a technique to estimate conditional quantile curves. It provides a comprehensive picture of a response contingent on explanatory variables. In a flexible modeling framework, a specific form of the conditional quantile curve is not a priori fixed. % Indeed, the majority of applications do not per se require specific functional forms. This motivates a local parametric rather than a global fixed model fitting approach. A nonparametric smoothing estimator of the conditional quantile curve requires to balance between local curvature and stochastic variability. In this paper, we suggest a local model selection technique that provides an adaptive estimator of the conditional quantile regression curve at each design point. Theoretical results claim that the proposed adaptive procedure performs as good as an oracle which would minimize the local estimation risk for the problem at hand. We illustrate the performance of the procedure by an extensive simulation study and consider a couple of applications: to tail dependence analysis for the Hong Kong stock market and to analysis of the distributions of the risk factors of temperature dynamics.