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

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
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