Quantile regression for functional partially linear model in ultra-high dimensions

Haiqiang Ma, Ting Li, Hongtu Zhu and Zhongyi Zhu

Computational Statistics & Data Analysis, 2019, vol. 129, issue C, 135-147

Abstract: Quantile regression for functional partially linear model in ultra-high dimensions is proposed and studied. By focusing on the conditional quantiles, where conditioning is on both multiple random processes and high-dimensional scalar covariates, the proposed model can lead to a comprehensive description of the scalar response. To select and estimate important variables, a double penalized functional quantile objective function with two nonconvex penalties is developed, and the optimal tuning parameters involved can be chosen by a two-step technique. Based on the difference convex analysis (DCA), the asymptotic properties of the resulting estimators are established, and the convergence rate of the prediction of the conditional quantile function can be obtained. Simulation studies demonstrate a competitive performance against the existing approach. A real application to Alzheimer’s Disease Neuroimaging Initiative (ADNI) data is used to illustrate the practicality of the proposed model.

Keywords: Asymptotic property; Double penalized quantile method; Functional partially linear quantile model; Functional principal component analysis; Variable selection (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:129:y:2019:i:c:p:135-147

DOI: 10.1016/j.csda.2018.06.005

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