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Consistency and asymptotic normality of profile-kernel and backfitting estimators in semiparametric reproductive dispersion nonlinear models. (English) Zbl 1176.62036

Summary: Semiparametric reproductive dispersion nonlinear models (SRDNM) are an extension of nonlinear reproductive dispersion models and semiparametric nonlinear regression models, and include semiparametric nonlinear models and semiparametric generalized linear models as its special cases. Based on the local kernel estimate of the nonparametric component, profile-kernel and backfitting estimators of parameters of interest are proposed in SRDNMs, and a theoretical comparison of both estimators is also investigated. Under some regularity conditions, strong consistency and asymptotic normality of the two estimators are proved. It is shown that the backfitting method produces a larger asymptotic variance than that for the profile-kernel method. A simulation study and a real example are used to illustrate the proposed methodologies.

MSC:

62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
65C60 Computational problems in statistics (MSC2010)
62J12 Generalized linear models (logistic models)
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