SMOOTH VARYING-COEFFICIENT ESTIMATION AND INFERENCE FOR QUALITATIVE AND QUANTITATIVE DATA
提出一种能同时处理定性和定量协变量的半参数变系数估计量，并给出模型正确设定的检验方法，通过数据驱动带宽选择提升有限样本效率。
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.