半参数变系数部分线性模型的函系数检验

华东师范大学学报(自然科学版) ›› 2009, Vol. 2009 ›› Issue (4): 54-61.

半参数变系数部分线性模型的函系数检验

黄振生

华东师范大学~~统计与精算学系，上海\quad 200241

收稿日期:2008-05-06 修回日期:2008-11-05 出版日期:2009-07-25 发布日期:2009-07-25
通讯作者: 黄振生

Tests for functional-coefficient parts on semiparametric varying-coefficient partially linear models

HUANG Zhen-sheng

Department of Statistics and Actuarial Science, East China Normal University,} } \EDWEI{{\it Shanghai} 200241, {\it China

Received:2008-05-06 Revised:2008-11-05 Online:2009-07-25 Published:2009-07-25
Contact: HUANG Zhen-sheng

摘要/Abstract

摘要： 通过局部线性方法给出未知函系数与未知参数的拟似然估计,
利用未知量的拟似然估计构造了函系数部分的广义似然比检验,
并证明了原假设下检验统计量渐近服从自由度独立讨厌参数与讨厌函数的~$\chi^{2}$-分布,
揭示了Wilks 现象. 通过模拟例子对给出的检验方法作出分析.

关键词: 局部线性方法, 拟似然估计, 广义似然比检验, Wilks 现象 , 局部线性方法, 拟似然估计, 广义似然比检验, Wilks 现象

Abstract: Based on the quasi-likelihood estimates obtained by the
local linear method,~the generalized likelihood ratio tests for the
models were established.~Under the null hypothesis the test
statistic followed asymptotically the $\chi^{2}$-distribution with
the scale constants and the degree of freedom being independent of
the nuisance parameters and the nuisance functions,~which was called
the Wilks phenomenon.~A simulated example was presented to
illustrate the proposed methods.

Key words: quasi-likelihood estimates, generalized likelihood ratio tests, Wilks phenomenon , local linear method, quasi-likelihood estimates, generalized likelihood ratio tests, Wilks phenomenon

中图分类号:

O212.7

黄振生. 半参数变系数部分线性模型的函系数检验[J]. 华东师范大学学报(自然科学版), 2009, 2009(4): 54-61.

HUANG Zhen-sheng. Tests for functional-coefficient parts on semiparametric varying-coefficient partially linear models [J]. Journal of East China Normal University(Natural Sc, 2009, 2009(4): 54-61.