Asymptotic distribution-free tests for semiparametric regressions

Escanciano, Juan Carlos;Pardo-Fernandez, Juan Carlos;Van Keilegom, Ingrid
(2015) , 33 pages

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Authors
  • Escanciano, Juan CarlosIndiana University, Bloomington, IN, USA
    Author
  • Pardo-Fernandez, Juan CarlosUniversity de Vigo, Spain
    Author
  • Van Keilegom, IngridUCLouvain
    Author
Abstract
This article proposes a new general methodology for constructing nonparametric asymptotic distribution-free tests for semiparametric hypotheses in regression models. Tests are based on the difference between the estimated restricted and unrestricted regression errors’ distributions. A suitable integral transformation of this difference renders the tests asymptotically distribution-free, with limits that are well-known functionals of a standard normal variable. Hence, the tests are straightforward to implement. The general methodology is illustrated with applications to testing for parametric models, semiparametric constrained mean-variance models and nonparametric significance. Several Monte Carlo studies show that the finite sample performance of the proposed tests is satisfactory in moderate sample sizes.
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Escanciano, J. C., Pardo-Fernandez, J. C., & Van Keilegom, I. (2015). Asymptotic distribution-free tests for semiparametric regressions (ISBA Discussion Paper 2015/01). https://hdl.handle.net/2078.5/195218