Abstract :
We propose a semiparametric varying-coefficient estimator that admits both qualitative
and quantitative covariates along with a test for correct specification of parametric
varying-coefficient models. The proposed estimator is exceedingly flexible
and has a wide range of potential applications including hierarchical (mixed) settings,
small area estimation, etc. A data-driven cross-validatory bandwidth selection
method is proposed that can handle both the qualitative and quantitative covariates
and that can also handle the presence of potentially irrelevant covariates, each of
which can result in finite-sample efficiency gains relative to the conventional frequency
(sample-splitting) estimator that is often found in such settings. Theoretical
underpinnings including rates of convergence and asymptotic normality are provided.
Monte Carlo simulations are undertaken to assess the proposed estimator’s
finite-sample performance relative to the conventional semiparametric frequency estimator
and to assess the finite-sample performance of the proposed test for correct
parametric specification.
