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June 2018 Asymptotic distribution-free tests for semiparametric regressions with dependent data
Juan Carlos Escanciano, Juan Carlos Pardo-Fernández, Ingrid Van Keilegom
Ann. Statist. 46(3): 1167-1196 (June 2018). DOI: 10.1214/17-AOS1581


This article proposes a new general methodology for constructing nonparametric and semiparametric Asymptotically Distribution-Free (ADF) tests for semiparametric hypotheses in regression models for possibly dependent data coming from a strictly stationary process. Classical tests based on the difference between the estimated distributions of the restricted and unrestricted regression errors are not ADF. In this article, we introduce a novel transformation of this difference that leads to ADF tests with well-known critical values. The general methodology is illustrated with applications to testing for parametric models against nonparametric or semiparametric alternatives, and semiparametric constrained mean–variance models. Several Monte Carlo studies and an empirical application show that the finite sample performance of the proposed tests is satisfactory in moderate sample sizes.


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Juan Carlos Escanciano. Juan Carlos Pardo-Fernández. Ingrid Van Keilegom. "Asymptotic distribution-free tests for semiparametric regressions with dependent data." Ann. Statist. 46 (3) 1167 - 1196, June 2018.


Received: 1 July 2016; Revised: 1 February 2017; Published: June 2018
First available in Project Euclid: 3 May 2018

zbMATH: 1392.62130
MathSciNet: MR3798000
Digital Object Identifier: 10.1214/17-AOS1581

Primary: 62E20 , 62G08 , 62G20 , 62H15

Keywords: Beta-mixing , error distribution , Goodness-of-fit tests , Local polynomial estimation , Nonparametric regression

Rights: Copyright © 2018 Institute of Mathematical Statistics


Vol.46 • No. 3 • June 2018
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