Backfitting and smooth backfitting for additive quantile models

TL;DR

This paper investigates backfitting methods for additive quantile models, demonstrating their asymptotic equivalence to mean regression estimators and analyzing their finite sample properties.

Contribution

It establishes the asymptotic equivalence of backfitting quantile estimators to mean regression estimators and evaluates their finite sample performance.

Findings

Backfitting quantile estimators are asymptotically equivalent to mean regression estimators.

Theoretical properties of quantile estimators mirror those of mean regression estimators.

Finite sample properties of the estimators are assessed.

Abstract

In this paper, we study the ordinary backfitting and smooth backfitting as methods of fitting additive quantile models. We show that these backfitting quantile estimators are asymptotically equivalent to the corresponding backfitting estimators of the additive components in a specially-designed additive mean regression model. This implies that the theoretical properties of the backfitting quantile estimators are not unlike those of backfitting mean regression estimators. We also assess the finite sample properties of the two backfitting quantile estimators.