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Consistency and asymptotic normality of profilekernel and backfitting estimators in semiparametric reproductive dispersion nonlinear models

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Abstract

Semiparametric reproductive dispersion nonlinear model (SRDNM) is an extension of nonlinear reproductive dispersion models and semiparametric nonlinear regression models, and includes semiparametric nonlinear model and semiparametric generalized linear model as its special cases. Based on the local kernel estimate of nonparametric component, profile-kernel and backfitting estimators of parameters of interest are proposed in SRDNM, and theoretical comparison of both estimators is also investigated in this paper. Under some regularity conditions, strong consistency and asymptotic normality of 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.

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Authors and Affiliations

  1. Department of Statistics, Yunnan University, Kunming, 650091, China

    NianSheng Tang, XueDong Chen & XueRen Wang

  2. Faculty of Science, Huzhou Normal College, Huzhou, 313000, China

    XueDong Chen

Authors
  1. NianSheng Tang
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  2. XueDong Chen
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  3. XueRen Wang
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Correspondence to NianSheng Tang.

Additional information

This work was supported by National Natural Science Foundation of China (Grant Nos. 10561008, 10761011), Natural Science Foundation of Department of Education of Zhejiang Province (Grant No. Y200805073), PhD Special Scientific Research Foundation of Chinese University (Grant No. 20060673002) and Program for New Century Excellent Talents in University (Grant No. NCET-07-0737)

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Tang, N., Chen, X. & Wang, X. Consistency and asymptotic normality of profilekernel and backfitting estimators in semiparametric reproductive dispersion nonlinear models. Sci. China Ser. A-Math. 52, 757–770 (2009). https://doi.org/10.1007/s11425-008-0148-2

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  • DOI: https://doi.org/10.1007/s11425-008-0148-2

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