Publication: Asymptotic distribution-free tests for semiparametric regressions with dependent data
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2018-06-01
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Institute of Mathematical Statistics
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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.
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Beta-mixing, Goodness-of-fit tests, Local polynomial estimation, Nonparametric regression, Error distribution
Bibliographic citation
Escanciano, J. C., Pardo-Fernández, J. C., & Van Keilegom, I. (2018). Asymptotic distribution-free tests for semiparametric regressions with dependent data.The Annals of Statistics, 46 (3), pp. 1167 - 1196