Estimation and inference of semi-varying coefficient models with heteroscedastic errors

• A consistent estimator of the variance function is proposed.
• Reweighting method is proposed to fit heteroscedastic semivarying coefficient models.
• Resulting constant coefficient estimates are proved to be asymptotically efficient.
• Performance of the estimation method is assessed by simulations.
• A practical data analysis is conducted.

This article focuses on the estimation of the parametric component, which is of primary interest, in semi-varying coefficient models with heteroscedastic errors. Specifically, we first present a procedure for estimating the variance function of the error term and the resulting estimator is proved to be consistent. Then, by applying the local linear smoothing technique, and taking the estimated error heteroscedasticity into account, we suggest a re-weighting estimation of the constant coefficients and the resulting estimators are shown to have smaller asymptotic variances than the profile least-squares estimators that neglect the error heteroscedasticity while remaining the same biases. Some simulation experiments are conducted to evaluate the finite sample performance of the proposed methodologies. Finally, a real-world data set is analyzed to demonstrate the application of the methods.