Efficient estimation for semivarying-coefficient models. (English) Zbl 1108.62019

Xia, Yingcun; Zhang, Wenyang; Tong, Howell

Biometrika 91, No. 3, 661-681 (2004).

Summary: 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.

MSC:

62F10	Point estimation
62G05	Nonparametric estimation
62H12	Estimation in multivariate analysis
62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G20	Asymptotic properties of nonparametric inference
62P12	Applications of statistics to environmental and related topics
62F12	Asymptotic properties of parametric estimators

Keywords:

Efficient estimator; Local linear; Semivarying-coefficient model; Strong alpha-mixing; Varying-coefficient model