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Moving window estimation procedures for additive regression function. (English) Zbl 0799.62040
Summary: The general additive regression function \(b(x) = \sum b_ j (x_ j)\) is considered and subjected to nonparametric estimation. The method of estimation is inspired by the regressogram approximations to the components of the regression function. The procedure using the moving window is then derived, it naturally generalizes to a kernel approach. The method can be applied to the likelihood-based models, in which the value of regression function is a parameter of the likelihood of a response variable \(Y\). The suggested moving window algorithm is a variant of T. Hastie and R. Tibshirani’s [Stat. Sci. 1, 297-318 (1986; Zbl 0645.62068)] local scoring procedure.
In order to discuss the quality of the obtained results, the method is compared with the approximation by regression splines, treated successfully by C. J. Stone [Ann. Stat. 14, 590-606 (1986; Zbl 0603.62050)]. An example illustrates the solution for the logistic regression, and the proportional hazard regression model is also examined.
62G07 Density estimation
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