Statistical inference for the functional quadratic quantile regression model

Gongming Shi, Tianfa Xie () and Zhongzhan Zhang
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Gongming Shi: Beijing University of Technology
Tianfa Xie: Beijing University of Technology
Zhongzhan Zhang: Beijing University of Technology

Metrika: International Journal for Theoretical and Applied Statistics, 2020, vol. 83, issue 8, No 4, 937-960

Abstract: Abstract In this paper, we develop statistical inference procedures for functional quadratic quantile regression model in which the response is a scalar and the predictor is a random function defined on a compact set of R. The functional coefficients are estimated by functional principal components. The asymptotic properties of the resulting estimators are established under mild conditions. In order to test the significance of the nonlinear term in the model, we propose a rank score test procedure. The asymptotic properties of the proposed test statistic are established. The proposed method provides a highly efficient and robust alternative to the least squares method, and can be conveniently implemented using existing R software package. Finally, we examine the performance of the proposed method for finite sample sizes by Monte Carlo simulation studies and illustrate it with a real data example.

Keywords: Quantile regression; Functional data; Functional quadratic regression; Rank score test; 62G08; 62G20 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00184-020-00763-5

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