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Efficient estimation of adaptive varying-coefficient partially linear regression model. (English) Zbl 1158.62031

Summary: An adaptive varying-coefficient partially linear regression (AVCPLR) model is proposed by combining a nonparametric regression model and a varying-coefficient regression model with different smoothing variables. It can be seen as a generalization of the varying-coefficient partially linear regression model, and it is also an example of a generalized structured model as defined by E. Mammen and J. P. Nielsen [Generalised structured models. Biometrika 90, 551–566 (2003)]. Based on the local linear technique and the marginal integrated method, the initial estimators of these unknown functions are obtained, each of which has big variance. To decrease the variances of these initial estimators, the one-step backfitting technique proposed by O. B. Linton [Efficient estimation of additive nonparametric regression models. Biometrika 84, No. 2, 469–473 (1997; Zbl 0882.62038)] is used to obtain the efficient estimators of all unknown functions for the AVCPLR model, and their asymptotic normalities are studied. Two simulated examples are given to illustrate the AVCPLR model and the proposed estimation methodology.

MSC:

62G08 Nonparametric regression and quantile regression
62E20 Asymptotic distribution theory in statistics

Citations:

Zbl 0882.62038

Software:

KernSmooth
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Full Text: DOI

References:

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