半参数非线性回归模型渐近推断的几何

本文利用Severini和Wong^[1]提出的最佳偏差曲线的概念,对半参数非线性回归模型建立了类似于Bates和Watts^[2]的几何结构。利用这个几何结构,我们研究了与统计曲率有关的某些渐近推断。文献中的许多结果^[3-6]被推广到半参数非线性回归模型。     

SOME ASYMPTOTIC INFERENCE IN MULTINOMIAL NONLINEAR MODELS （A GEOMETRIC APPROACH）

ＳＯＭＥＡＳＹＭＰＴＯＴＩＣＩＮＦＥＲＥＮＣＥＩＮＭＵＬＴＩＮＯＭＩＡＬＮＯＮＬＩＮＥＡＲＭＯＤＥＬＳ（ＡＧＥＯＭＥＲＩＣＡＰＰＲＯＡＣＨ）￥ＷＥＩＢＯＣＨＥＮＧ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｏｕｔｈｅａｓｔＵｎｉｖｅｒｓｉｔｙ...     

ON CONFIDENCE REGIONS OF SEMIPARAMETRIC NONLINEAR REGRESSION MODELS(A GEOMETRIC APPROACH)

1IntroductionSelltipaxanetricmodelsaxemodelscolltaillingbothparametricalldnonparametriccom-pOnents,wl1erethenol1parametriccomponentplaystheroleofanusianceparameter.Moreprecisely,asellliparametriclllodelisparameterizedbyaparameterofillteresttakingvaI1lesinfinite-din1el1sionajEuclidenspaceal1danusianceparantetertakingvaluesininfinite-dimellsionalspace.Tl1ismodelembodiesacolllpro11tisebetweenemployingagelleralnonparametricspeci-ficatioll.wl1ich,iftheconditiol1il1gvariablesarehighdimensional,woul…     

纵向数据下部分非线性模型的广义经验似然推断

本文研究了纵向数据下部分非线性模型中未知参数的置信域的构造.利用经验似然方法,构造了非线性函数中未知参数的广义对数经验似然比统计量,证明了其渐近于卡方分布.同时,得到了未知参数的最大经验似然估计,并证明了其渐近正态性.     

拟似然非线性模型的某些渐近推断:几何方法

Abstract. A modified Bates and Watts geometric framework is proposed for quasi-likelihoodnonlinear models in Euclidean inner product space. Based on the modified geometric framework,some asymptotic inference in terms of curvatures for quasi-likelihood nonlinear models is stud-ied. Several previous results for nonlinear regression models and exponential family nonlinearmodels etc. are extended to quasi-likelihood nonlinear models.     

核实数据下非线性EV模型中经验似然降维推断

本文研究了响应变量有误差的非线性模型.应用半参数降维技术构造未知参数的被估计经验似然及调整的经验似然,证明了所提出的被估计的经验对数似然与其调整的经验对数似然分别渐近于独立卡方变量加权和的分布与标准卡方分布,所得结果可用来构造未知参数的置信域.     

非线性E-V回归模型中参数估计的渐近性质

本文讨论了非线性E-V回归模型中参数的估计问题,构造了未知参数β0的最小二乘估计β和误差方差σ2的估计σ2,证明了β具有渐近正态性,同时也证明了σ2依概率收敛于σ2的速度可达到n-1/2.     

非线性随机效应模型的异方差性检验

随机效应模型广泛应用于刻画重复测量数据的特征．在该模型中,随机误差的方差包括受试群体内部及受试群体之间两项方差．Ｚｈａｎｇ和 Ｗｅｉｓｓ ２０００年研究了线性随机效应模型的异方差检验,本文对非线性随机效应模型,分别讨论了群体内、群体间和多变量的异方差性的检验问题,得到了检验的ｓｃｏｒｅ统计量,并讨论了三种情形下,相应的ｓｃｏｒｅ函数之间的关系．最后给出一个数值例子说明上述方法的有用性．     

JUMP DETECTION BY WAVELET IN NONLINEAR AUTOREGRESSIVE MODELS

1991MRSubjectClassification62G05,62G201IntroductionDtttectiollofthe.iulnppointshasrecentlyfoundinCleasillginterests.Sincejllliippoillts(\andftstfriheson-iesuddenchallgephenorxlenonena,theyal'every11seflllillrllodellillgpracticalprobl(!lusarisinginfieldssuchaseconomics,signalanalysis,illlageprocessingandphonetici'lentification.TheeallyworkondetectiollofthejumpsisShi..[1]andSpeckman[2].Yin[']consideredthe1llodely(t)=s(t) e(f),05t51,(1.1)wheree(t)isaGaussianwhitenoisewithe(0)=0ands(f)isadeter…     

A STRONG ERGODIC THEOREM FOR SOME NONLINEAR MATRIX MODELS FOR THE DYNAMICS OF STRUCTURED POPULATIONS

A general class of matrix difference equation models for the dynamics of discrete class structured populations in discrete time which possess a certain general type of nonlinearity introduced by Leslie for age-structured populations is considered. Arbitrary structuring is allowed in that transitions between any two classes are permitted. It is shown that normalized class distributions for such nonlinear models globally approach a “stable class distribution” and thus possess a strong ergodic property exactly like that of the classical linear theory of demography. However, unlike in the linear theory according to which the total population size grows or dies exponentially, the dynamics of total population size in these nonlinear models are shown to be governed by a nonlinear, nonautonomous scalar difference equation. This difference equation is asymptotically autonomous, and theorems which relate the dynamics of total population size to those of this limiting equation are proved. Examples in which the results are applied to some nonlinear age-structure models found in the literature are given.     

具有双线性BL(1,1,1,1)误差的非线性回归模型相关性和方差齐性的检验

在时间序列回归模型分析中,相关性和方差齐性的检验是一个很基本的问题.本文讨论了具有双线性BL(1,1,1,1)误差的非线性回归模型的相关性和方差齐性的检验问题, 用Score检验方法给出了双线性项检验、相关性检验、方差齐性检验、以及相关性和方差齐性同时检验的检验统计量.推广和发展了具有线性序列误差项回归模型的结果.本文还用数值实例说明了检验方法的实用价值.     

非线性再生散度模型参数置信域的曲率表示

本文对非线性再生散度模型在Ｅｕｃｌｉｄ空间建立了几何结构。在此基础上,研究了该模型参数和子集参数的三种近似置信域,推广了Ｈａｍｉｌｔｏｎ和韦博成等人的工作。     

一类催化反应中的非线性奇摄动边值问题的渐近解

本文研究了催化反应非线性奇摄动边值问题．利用微分不等式理论和方法，得到了问题的解的任意次近似渐近估计．     

TESTING FOR VARYING DISPERSION OF LONGITUDINAL BINOMIAL DATA IN NONLINEAR LOGISTIC MODELS WITH RANDOM EFFECTS

In this paper, it is discussed that two tests for varying dispersion of binomial data in the framework of nonlinear logistic models with random effects, which are widely used in analyzing longitudinal binomial data. One is the individual test and power calculation for varying dispersion through testing the randomness of cluster effects, which is extensions of Dean(1992) and Commenges et al (1994). The second test is the composite test for varying dispersion through simultaneously testing the randomness of cluster effects and the equality of random-effect means. The score test statistics are constructed and expressed in simple, easy to use, matrix formulas. The authors illustrate their test methods using the insecticide data (Giltinan, Capizzi & Malani (1988)).     

误差服从多元t分布的一类线性模型下参数估计的若干注记

研究一类线性模型下参数估计的若干问题．这类模型包含了多个因变量线性模型、增长曲线模型、扩充的增长曲线模型、似乎不相关回归方程组、方差分量模型等常用模型．在这类线性模型下,证明了当误差服从多元t分布时与误差服从多元正态分布时,具有相同的完全统计量和无偏估计,且在后一种情况下的充分统计量必为前一种情况下的充分统计量．对于带有多种协方差结构的前述几种模型,把在误差服从多元正态分布下,相应的协方差阵及有关参数的一致最小风险无偏(UMRU)估计存在性的结论推广到了相应的误差服从多元t分布情形．此外,对于误差服从多元t分布的这类统一的线性模型,给出了回归系数的线性可估函数的无偏估计的协方差阵的C-R下界．