Adaptive-weighted estimation of semi-varying coefficient models with heteroscedastic errors

摘要

An adaptive-weighted estimation procedure for parametric and nonparametric coefficients in semi-varying coefficient models with heteroscedastic errors is considered in this paper. Firstly, we present a consistent estimator of the variance function of the error term. In order to take the heteroscedasticity into consideration, we consider the weighted local linear smoothing technique. Asymptotic properties of the proposed estimators are established. Our theoretical results demonstrate that the adaptive-weighted estimator is more efficient than the unweighted profile least-squares estimators. The simulation results show that our adaptive-weighted estimators are more efficient, compared to profile least-squares estimators and re-weighted estimators under the finite sample size. Finally, our estimation procedure is applied to a real-world data.