Non-parametric Quantile Regression and Uniform Inference with Unknown Error Distribution
Year: 2025
Type: preprint
Abstract: This paper studies the non-parametric estimation and uniform inference for the conditional quantile regression function (CQRF) with covariates exposed to measurement errors. We consider the case that the distribution of the measurement error is unknown and allowed to be either ordinary or super smooth. We estimate the density of the measurement error by the repeated measurements and propose the deconvolution kernel estimator for the CQRF. We derive the uniform Bahadur representation of the proposed estimator and construct the uniform confidence bands for the CQRF, uniformly in the sense for all covariates and a set of quantile indices, and establish the theoretical validity of the proposed inference. A data-driven approach for selecting the tuning parameter is also included. Monte Carlo simulations and a real data application demonstrate the usefulness of the proposed method.
Source: arXiv (Cornell University)
Authors: Hou, Haoze, Huang, Wei, Zhang, Zheng
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6891838411
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