Electronic Journal of Statistics

Quantile processes for semi and nonparametric regression

Shih-Kang Chao, Stanislav Volgushev, and Guang Cheng

Full-text: Open access

Abstract

A collection of quantile curves provides a complete picture of conditional distributions. A properly centered and scaled version of the estimated curves at various quantile levels gives rise to the so-called quantile regression process (QRP). In this paper, we establish weak convergence of QRP in a general series approximation framework, which includes linear models with increasing dimension, nonparametric models and partial linear models. An interesting consequence is obtained in the last class of models, where parametric and non-parametric estimators are shown to be asymptotically independent. Applications of our general process convergence results include the construction of non-crossing quantile curves and the estimation of conditional distribution functions. As a result of independent interest, we obtain a series of Bahadur representations with exponential bounds for tail probabilities of all remainder terms. Bounds of this kind are potentially useful in analyzing statistical inference procedures under the divide-and-conquer setup.

Article information

Source
Electron. J. Statist. Volume 11, Number 2 (2017), 3272-3331.

Dates
Received: March 2017
First available in Project Euclid: 2 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1506931550

Digital Object Identifier
doi:10.1214/17-EJS1313

Zentralblatt MATH identifier
1373.62151

Subjects
Primary: 62F12: Asymptotic properties of estimators 62G20: Asymptotic properties 62G08: Nonparametric regression

Keywords
Bahadur representation quantile regression process semi/nonparametric model series estimation

Rights
Creative Commons Attribution 4.0 International License.

Citation

Chao, Shih-Kang; Volgushev, Stanislav; Cheng, Guang. Quantile processes for semi and nonparametric regression. Electron. J. Statist. 11 (2017), no. 2, 3272--3331. doi:10.1214/17-EJS1313. https://projecteuclid.org/euclid.ejs/1506931550


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