This paper proposes a consistent test for the goodness-of-fit of
parametric regression models that overcomes two important problems
of the existing tests, namely, the poor empirical power and size
performance of the tests due to the curse of dimensionality and the
subjective choice of parameters such as bandwidths, kernels, and
integrating measures. We overcome these problems by using a residual
marked empirical process based on projections (RMPP). We study the
asymptotic null distribution of the test statistic, and we show that
our test is able to detect local alternatives converging to the null
at the parametric rate. It turns out that the asymptotic null
distribution of the test statistic depends on the data generating
process, and so a bootstrap procedure is considered. Our bootstrap
test is robust to higher order dependence, in particular to
conditional heteroskedasticity. For completeness, we propose a new
minimum distance estimator constructed through the same RMPP as in
the testing procedure. Therefore, the new estimator inherits all the
good properties of the new test. We establish the consistency and
asymptotic normality of the new minimum distance estimator. Finally,
we present some Monte Carlo evidence that our testing procedure can
play a valuable role in econometric regression modeling.The author thanks Carlos Velasco and
Miguel A. Delgado for useful comments. The paper has also
benefited from the comments of two referees and the co-editor.
This research was funded by the Spanish Ministry of Education
and Science reference number SEJ2004-04583/ECON and by the
Universidad de Navarra reference number 16037001.