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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.

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
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