基于连续可分的广义非线性纵向数据模型偏离名义离差的score检验及其功效  

Score Tests and Powers for Departures from Nominal Dispersion in Separable and Continuous Generalized Nonlinear Models with Longitudinal Data

作　　者：林金官[1] 李勇[2] 韦博成[1] 

机构地区：[1]东南大学数学系,南京210096 [2]中山大学管理学院财务与投资系,广州510275

出　　处：《应用数学学报》2009年第1期60-74,共15页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10671032);江苏省自然科学基金(BK2008284)资助项目．

摘　　要：指数族非线性模型或广义非线性模型是广义线性模型和正态回归模型的自然推广.本文针对可分的连续型指数族回归模型(如正态模型,Γ模型,逆高斯模型),讨论广义非线性纵向数据模型中偏离名义离差的检验问题,得到了检验的score统计量,并推导了它们的渐近分布和局部近似功效.然后利用Monte Carlo方法研究了检验统计量的性质.最后利用百慕大草地数据说明了检验方法的应用.Exponential family nonlinear models, or generalized nonlinear models are generalized from generalized linear models and nonlinear regression. For separable and continous exponential family models （such as normal, gamma, and inverse Gaussian models）, this paper discusses the tests for departures from nominal dispersion in the framework of longitudinal nonlinear models with varying dispersion and/or random effects. The score test statistics are constructed and their asymptotic distributions and local powers are derived. The properties of test statistics are investigated through Monte Carlo simulations. We illustrate our test methods by data concerning the yield of coastal Bermuda grass.

关 键 词：纵向数据 可分的广义非线性模型 名义离差 SCORE检验 模拟功效 

分 类 号：O212.2[理学—概率论与数理统计]