Abstract

Linear quantile regression model assumes quantiles of a response at

certain levels are linearly related with covariates. If the model is assumed for

one single quantile level, the semiparametric efficient estimation involves estimation of the conditional density of an error given covariates, which could be

prohibitively difficult because of the curse of dimensionality.

However, if the

model is assumed for all quantile levels, estimation of conditional density becomes estimation of the derivative of regression coefficient functions, which is

naturally available from initial estimators such as the Koenker-Bassett estimator. This paper derives the semiparametric efficient scores and the corresponding

efficiency bounds for the regression coefficients. Although there is no closed form

expression of the estimator or estimating function, we propose a computationally

feasible procedure leading to semiparametrically efficient estimation. Simulation

studies show that the proposed method could lead to substantial efficiency gain

over the standard methods.

Key words and phrases: Quantile regression; Semiparametric efficient score; Least favorable submodel; One-step estimation

Information

Preprint No.SS-2024-0378
Manuscript IDSS-2024-0378
Complete AuthorsZhanfeng Wang, Kani Chen, Yuanyuan Lin, Zhiliang Ying
Corresponding AuthorsKani Chen
Emailsmakchen@ust.hk

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Acknowledgments

The authors thank the Editor, the Associate Editor and two anonymous

reviewers for their insightful comments and constructive suggestions that

helped improve the paper significantly. Z. Wang’s research was supported

by the National Science Foundation of China (No. 12371277, No. 12231017).

Y. Lin’s research was partially supported by the Hong Kong Research

Grants Council (No. 14306620 and 14304523), and Direct Grants for Research, The Chinese University of Hong Kong.

Supplementary Materials

The supplementary material contains the proofs of all theorems and additional results from numerical studies.

Supplementary materials are available for download.