Inference for Partially Linear Quantile Regression Models in Ultrahigh Dimension

Abstract

Conditional quantile regression provides a useful statistical tool for modeling and inferring the relationship between the response and covariates in the heterogeneous data. In this paper, we develop a novel testing procedure for the ultrahigh-dimensional partially linear quantile regression model to investigate the significance of ultrahigh-dimensional interested covariates in the presence of ultrahigh-dimensional nuisance covariates. The proposed test statistic is an

L_2

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-type statistic. We estimate the nonparametric component by some flexible machine learners to handle the complexity and ultrahigh dimensionality of considered models. We establish the asymptotic normality of the proposed test statistic under the null and local alternative hypotheses. A screening-based testing procedure is further provided to make our test more powerful in practice under the ultrahigh-dimensional regime. We evaluate the finite-sample performance of the proposed method via extensive simulation studies. A real application to a breast cancer dataset is presented to illustrate the proposed method.

Keywords

Semiparametric model / Significance testing / Quantile regression / Ultrahigh dimensionality / 63F03 / 62F35 / 62H15

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Funding

National Natural Science Foundation of China(12071038)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature