Efficient estimation for semivarying-coefficient models

Motivated by two practical problems, we propose a new procedure for estimating a semivarying-coefficient model. Asymptotic properties are established which show that the bias of the parameter estimator is of order h(3) when a symmetric kernel is used, where h is the bandwidth, and the variance is of order n(-1) and efficient in the semiparametric sense. Undersmoothing is unnecessary for the root-n consistency of the estimators. Therefore, commonly used bandwidth selection methods can be employed. A model selection method is also developed. Simulations demonstrate how the proposed method works. Some insights are obtained into the two motivating problems by using the proposed models.