非线性半参数EV模型的最大经验似然估计

数学物理学报 ›› 2012, Vol. 32 ›› Issue (4): 729-743.

非线性半参数EV模型的最大经验似然估计

冯三营^1,2, 薛留根¹

1.北京工业大学应用数理学院北京 |100022;
2.洛阳师范学院数学科学学院河南洛阳 471022

收稿日期:2010-04-09 修回日期:2011-09-03 出版日期:2012-08-25 发布日期:2012-08-25
基金资助:
国家自然科学基金(11171012, 11101014, 11001118)、国家社科基金(11CTJ004)、北京市优秀博士学位论文指导教师科技项目(20111000503)和洛阳师范学院青年基金 (2010-QNJJ-001)资助

Maximum Empirical Likelihood Estimators in Nonlinear Semiparametric EV Regression Models

FENG San-Ying^1,2, XUE Liu-Gen¹

1.College of Applied Sciences, Beijing University of Technology, Beijing 100022;
2.College of Mathematics and Science, Luoyang Normal University, Henan Luoyang 471022

Received:2010-04-09 Revised:2011-09-03 Online:2012-08-25 Published:2012-08-25
Supported by:
国家自然科学基金(11171012, 11101014, 11001118)、国家社科基金(11CTJ004)、北京市优秀博士学位论文指导教师科技项目(20111000503)和洛阳师范学院青年基金 (2010-QNJJ-001)资助

摘要/Abstract

摘要：

考虑非参数协变量带有测量误差(EV)的非线性半参数模型, 在测量误差分布为普通光滑分布时, 利用经验似然方法, 给出了回归系数, 光滑函数以及误差方差的最大经验似然估计. 在一定条件下证明了所得估计量的渐近正态性和相合性. 最后通过数值模拟研究了所提估计方法在有限样本下的实际表现.

关键词: 非线性半参数模型, 测量误差, 经验似然, 普通光滑, 渐近正态性

Abstract:

In this paper, we consider the nonlinear semiparametric models with measurement error in the nonparametric part. When the error is ordinarily smooth, we obtain the maximum empirical likelihood estimators of regression coefficient, smooth function and error variance by using the empirical likelihood method. The asymptotic normality and consistency of the proposed estimators are proved under some appropriate conditions. Finite sample performance of the proposed method is illustrated in a simulation study.

Key words: Nonlinear semiparametric model, Errors in variables, Empirical likelihood, Ordinarily smooth, Asymptotic normality

中图分类号:

62G05

冯三营, 薛留根. 非线性半参数EV模型的最大经验似然估计[J]. 数学物理学报, 2012, 32(4): 729-743.

FENG San-Ying, XUE Liu-Gen. Maximum Empirical Likelihood Estimators in Nonlinear Semiparametric EV Regression Models[J]. Acta mathematica scientia,Series A, 2012, 32(4): 729-743.

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