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2017 Quantile processes for semi and nonparametric regression
Shih-Kang Chao, Stanislav Volgushev, Guang Cheng
Electron. J. Statist. 11(2): 3272-3331 (2017). DOI: 10.1214/17-EJS1313


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.


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Shih-Kang Chao. Stanislav Volgushev. Guang Cheng. "Quantile processes for semi and nonparametric regression." Electron. J. Statist. 11 (2) 3272 - 3331, 2017.


Received: 1 March 2017; Published: 2017
First available in Project Euclid: 2 October 2017

zbMATH: 1373.62151
MathSciNet: MR3708539
Digital Object Identifier: 10.1214/17-EJS1313

Primary: 62F12 , 62G08 , 62G20

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


Vol.11 • No. 2 • 2017
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