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Abstract
In this paper, we consider the problem of testing the significance of covariates in a nonparametric regression model. We propose to use some bootstrap procedures to better approximate the finite sample distribution of the test statistics. We establish the asymptotic validity of the proposed bootstrap procedures. Simulation results show that the bootstrap tests successfully overcome the finite sample size distortions of the tests based on critical values obtained from the asymptotic null distributions.
Acknowledgements
We would like to thank an anonymous referee for the instructive comments. Dingding Li's research was partially supported by SSHRC of Canada.
Notes
¶Bierens Citation19 is the first to propose a consistent test for a parametric regression functional form. Using nonparametric estimation techniques to construct consistent model specification tests was first suggested by Ullah Citation20.
†Here we only give a sufficient condition for
Equation(1)
, which is convenient to use in our context. For a rigorous definition of
Equation(1)
, see Citation31.