华东师范大学学报(自然科学版) ›› 2011, Vol. 2011 ›› Issue (3): 1-11.

• 应用数学与基础数学 •    下一篇

半参数非线性模型中的t-型估计和影响分析

姜 荣1; 邵明江2; 钱伟民1   

  1. 1. 同济大学 应用数学系, 上海 200092;2. 华东师范大学 数学系, 上海 200062
  • 收稿日期:2010-06-01 修回日期:2010-09-01 出版日期:2011-05-25 发布日期:2011-05-25
  • 通讯作者: 钱伟民

t-type estimators and influence diagnostics in semiparametric nonlinear models

JIANG Rong1; SHAO Ming-jiang2 , QIAN Wei-min1

  

  1. 1. Department of Mathematics, Tongji University, Shanghai 200092, China 2. Department of Mathematics, East China Normal University, Shanghai 200062, China
  • Received:2010-06-01 Revised:2010-09-01 Online:2011-05-25 Published:2011-05-25
  • Contact: QIAN Wei-min

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摘要： 给出半参数非线性回归模型的t-型估计及其EM算法, 同时获得估计的相合性及渐近正态性. 并基于EM算法中的Q函数, 研究了半参数非线性回归模型的统计诊断方法. 最后, 用一个模拟例子和一个实际例子验证了本文提出的t-型估计和诊断方法的有效性.

关键词: 半参数模型, 非线性模型, t-型回归估计, Cook距离, 局部影响分析, P-样条, EM算法, 半参数模型, 非线性模型, t-型回归估计, Cook距离, 局部影响分析, P-样条, EM算法

Abstract: t-type regression estimators for the semiparametric nonlinear models were defined, and the EM algorithm for the t-type estimators were given. Moreover, the consistency of t-type regression estimators was obtained. And on the basis of the Q-function in the EM algorithm, statistical diagnostics methods were investigated. Finally, the proposed algorithm was tested by simulation analysis and by a real data sample.

Key words: nonlinear model, t-type regression estimator, Cook distance, local influence, penalized spline, EM algorithm, semiparametric regression, nonlinear model, t-type regression estimator, Cook distance, local influence, penalized spline, EM algorithm

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