Quantile index regression

TL;DR

This paper introduces a flexible quantile index regression model that improves tail estimation in high-dimensional data, supported by theoretical analysis, simulations, and real data application.

Contribution

It proposes a novel parametric structure for tail estimation and combines composite quantile regression to ensure non-crossing estimators with proven theoretical properties.

Findings

The model effectively estimates tail structures with rich observations.

Theoretical results include asymptotic normality and non-asymptotic error bounds.

Simulation and empirical studies demonstrate the model's practical usefulness.

Abstract

Estimating the structures at high or low quantiles has become an important subject and attracted increasing attention across numerous fields. However, due to data sparsity at tails, it usually is a challenging task to obtain reliable estimation, especially for high-dimensional data. This paper suggests a flexible parametric structure to tails, and this enables us to conduct the estimation at quantile levels with rich observations and then to extrapolate the fitted structures to far tails. The proposed model depends on some quantile indices and hence is called the quantile index regression. Moreover, the composite quantile regression method is employed to obtain non-crossing quantile estimators, and this paper further establishes their theoretical properties, including asymptotic normality for the case with low-dimensional covariates and non-asymptotic error bounds for that with high-dimensional covariates. Simulation studies and an empirical example are presented to illustrate the usefulness of the new model.