Improved Quantile Regression Estimators when the Errors are Independently and Non-identically Distributed

TL;DR

This paper proposes new quantile regression estimators using preliminary testing and shrinkage methods to improve robustness when error terms are independent but not identically distributed, supported by simulations and real data.

Contribution

It introduces novel estimation strategies for quantile regression under i.ni.d. errors, including asymptotic analysis and comparisons with penalized methods.

Findings

Proposed estimators outperform classical methods in non-i.i.d. error scenarios.

Simulation results show improved accuracy over LSE and penalized estimators.

Real data example demonstrates practical applicability of the methods.

Abstract

In a classical regression model, it is usually assumed that the explanatory variables are independent of each other and error terms are normally distributed. But when these assumptions are not met, situations like the error terms are not independent or they are not identically distributed or both of these, LSE will not be robust. Hence, quantile regression has been used to complement this deficiency of classical regression analysis and to improve the least square estimation (LSE). In this study, we consider preliminary test and shrinkage estimation strategies for quantile regression models with independently and non-identically distributed (i.ni.d.) errors. A Monte Carlo simulation study is conducted to assess the relative performance of the estimators. Also, we numerically compare their performance with Ridge, Lasso, Elastic Net penalty estimation strategies. A real data example is presented to illustrate the usefulness of the suggested methods. Finally, we obtain the asymptotic results of suggested estimators