## The Annals of Statistics

### Asymptotic distribution-free tests for semiparametric regressions with dependent data

#### Abstract

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.

#### Article information

Source
Ann. Statist., Volume 46, Number 3 (2018), 1167-1196.

Dates
Revised: February 2017
First available in Project Euclid: 3 May 2018

https://projecteuclid.org/euclid.aos/1525313079

Digital Object Identifier
doi:10.1214/17-AOS1581

Mathematical Reviews number (MathSciNet)
MR3798000

Zentralblatt MATH identifier
1392.62130

#### Citation

Escanciano, Juan Carlos; Pardo-Fernández, Juan Carlos; Van Keilegom, Ingrid. Asymptotic distribution-free tests for semiparametric regressions with dependent data. Ann. Statist. 46 (2018), no. 3, 1167--1196. doi:10.1214/17-AOS1581. https://projecteuclid.org/euclid.aos/1525313079

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#### Supplemental materials

• Supplement to “Asymptotic distribution-free tests for semiparametric regressions with dependent data”. The supplement contains further Monte Carlo simulations and the proofs of some asymptotic results.