Statistics and Its Interface

Volume 16 (2023)

Number 4

SIMEX estimation for quantile regression model with measurement error

Pages: 545 – 552

DOI: https://dx.doi.org/10.4310/22-SII742

Authors

Yiping Yang (School of Mathematics and Statistics, Chongqing Technology and Business University, Chongquing, China; and Chongqing Key Laboratory of Social Economic and Applied Statistics, Chongqing, China)

Peixin Zhao (School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, China)

Dongsheng Wu (School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, China)

Abstract

The quantile regression model with measurement error is considered. To deal with measurement error, we extend the simulation-extrapolation (SIMEX) method to the case of quantile regressions in the presence of covariate measurement error. The proposed SIMEX estimation corrects the bias caused by the measurement error, and not requires the equal distribution assumption of the regression error and measurement error. The asymptotic distribution of the proposed estimator is derived. The finite sample performance of the proposed method is investigated by a simulation study. A real dataset from the Framingham Heart Study is analyzed to illustrate the proposed method.

Keywords

quantile regression, measurement error, simulation-extrapolation, correction for attenuation

2010 Mathematics Subject Classification

Primary 62G05. Secondary 62G20.

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Yiping Yang’s research was supported by Chongqing Natural Science Foundation (cstc2021jcyj-msxmX0079) and Humanities and Social Sciences Program of Chongqing Education Commission (21SIGH118).

Peixin Zhao’s research was supported by Chongqing Natural Science Foundation (cstc2020jcyjmsxmX0006) and the National Social Science Foundation of China (18BTJ035).

Received 21 December 2021

Accepted 24 May 2022

Published 14 April 2023