Abstract :
Semiparametric methods are widely employed in applied work where the ability
to conduct inferences is important. To establish asymptotic normality for making
inferences, bias control mechanisms are often used in implementing semiparametric
estimators. The first contribution of this paper is to propose a mechanism that enables
us to establish asymptotic normality with regular kernels. In so doing, we argue that
the resulting estimator performs very well in finite samples.
Semiparametric models are commonly estimated under a single index assumption.
Because the consistency of the estimator critically depends on this assumption being
correct, our second objective is to develop a test for it. To ensure that the test statistic
has good size and power properties in finite samples, we employ a bias control
mechanism similar to that underlying the estimator. Furthermore, we structure the
test so that its form adapts to the model under the alternative hypothesis. Monte Carlo
results confirm that the bias control and the adaptive feature significantly improve
the performance of the test statistic in finite samples.
