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Efficient estimation of a semiparametric partially linear varying coefficient model. (English) Zbl 1064.62043
Summary: We propose a general series method to estimate a semiparametric partially linear varying coefficient model. We establish the consistency and $$\sqrt n$$-normality property of the estimator of the finite-dimensional parameters of the model. We further show that, when the error is conditionally homoskedastic, this estimator is semiparametrically efficient in the sense that the inverse of the asymptotic variance of the estimator of the finite-dimensional parameter reaches the semiparametric efficiency bound of this model.
A small-scale simulation is reported to examine the finite sample performance of the proposed estimator, and an empirical application is presented to illustrate the usefulness of the proposed method in practice. We also discuss how to obtain an efficient estimation result when the error is conditional heteroskedastic.

##### MSC:
 62G08 Nonparametric regression and quantile regression 62G20 Asymptotic properties of nonparametric inference 65C05 Monte Carlo methods
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