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Corrected-loss estimation for quantile regression with covariate measurement errors. (English) Zbl 1239.62047
Summary: We study estimation in quantile regression when covariates are measured with errors. Existing methods require stringent assumptions, such as spherically symmetric joint distributions of the regression and measurement error variables, or linearity of all quantile functions, which restrict model flexibility and complicate computation. We develop a new estimation approach based on corrected scores to account for a class of covariate measurement errors in quantile regression. The proposed method is simple to implement. Its validity requires only linearity of the particular quantile function of interest, and it requires no parametric assumptions on the regression error distributions. Finite-sample results demonstrate that the proposed estimators are more efficient than the existing methods in various models considered.

62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
65C60 Computational problems in statistics (MSC2010)
62J05 Linear regression; mixed models
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