非线性模型中的拟似然估计和约束拟似然估计

该文证明了,在非线性回归模型中,若以均方误差或均方误差矩阵为标准,拟似然估计是正则广义拟似然估计类中的最优估计,并讨论了拟得分函数最优性与拟似然估计最优性的关系.为改进拟似然估计,该文提出了一种约束拟似然估计,并证明了约束拟似然估计比拟似然估计有较小的均方误差.     

非线性模型中拟似然估计的若干性质

本文主要讨论拟得分函数在广义正则线性无偏函数类中的性质，并证明拟似然估计在泛似拟然估计类中的渐近最优性。     

相依非线性回归系统中的附加信息Bayes拟似然

对多个相依统计模型的研究,现有成果主要集中在相依线性回归系统.本文则首次提出多个相依非线性回归系统中的附加信息Bayes拟似然,给出误差相关信息和先验信息在拟似然中的迭加方法,在较弱的条件下得到附加信息Bayes拟似然的一些性质,在Bayes风险准则下。讨论了其估计函数和参数估计的最优性,证明了附加信息Bayes拟似然的渐近 Bayes风险随着相依信息的增力。而逐步减少.     

拟似然非线性模型中MQLE的弱相合性的充分条件

拟似然非线性模型包括广义线性模型作为一个特殊情形.给出了拟似然非线性模型中极大拟似然估计的弱相合性的一些充分条件,其中矩的条件要弱于文献中极大拟似然估计的强相合性的条件.     

广义线性模型中一类推广的拟似然估计与异方差性诊断检验

本文考虑了随机设计情形下一类普通的异方差回归模型，在这个模型中，假定回归函数与方差函数之间的关系服从推广的广义非线性模型，该模型在实际中很常见，广义线性模型便是其特例，首先，我们导出了均值函数的局部加权拟似然估计，然后，用它来得到方差函数的估计，并且证明了这些估计有较好的性质，最后，建立了异方差检验统计量，文中的方法很吸引人。     

非线性回归模型的经验似然诊断

经验似然方法已经被广泛用于线性模型和广义线性模型.本文基于经验似然方法对非线性回归模型进行统计诊断.首先得到模型参数的极大经验似然估计;其次基于经验似然研究了三种不同的影响曲率度量;最后通过一个实际例子,说明了诊断方法的有效性.     

线性约束下异方差回归模型参数的极大似然估计

运用参数的极大似然估计法,给出在线性约束条件Hβ=C下异方差回归模型参数β和λ的极大似然估计,并讨论了估计参数的性质和模型的残差.利用得到的结论对线性约束下异方差回归模型的进一步研究和应用具有一定的理论和实际价值.     

最大似然估计的一个推广

我们常常会遇到最大似然估计不存在的情况,这种情况以在非正态回归模型中最为典型。当参数向量不能被估计时,人们对参数向量的线性函数的估计饶有兴趣。本文给出了这些线性函数的广义最大似然估计的定义,讨论了它的性质,并得到了利用投影变换确定具有有限广义最大似然估计的线性函数的方法。最后,通过几个常见的定性资料统计模型的实例,展现了求广义最大似然估计的实施过程。     

基于ARFIMA-GARCH模型的混成检验

本文研究了ARFIMA-GARCH模型的混成检验问题.基于拟极大指数似然估计,给出了平方残差自相关函数的渐近性,进而建立了基于平方残差自相关函数的混成检验统计量.通过实例分析,表明可利用基于平方残差自相关函数的混成检验统计量来诊断检验由拟极大指数似然估计方法拟合的ARFIMA-GARCH模型.     

广义线性模型参数的自适应拟似然估计

对广义线性模型参数的一种拟似然估计的理论给予了彻底的处理. 在该估计中,响应变量的未知的协方差阵是通过样本去估计的.证明了所定义的估计量具有下述意义上的渐近有效性：当样本量n→∞时, 该估计有渐近正态性,且其极限分布的协方差阵重合于当响应变量的协方差阵完全已知时,拟似然估计的极限分布的协方差阵.     

CONSERVATIVE ESTIMATING FUNCTIONIN THE NONLINEAR REGRESSION MODEL WITHAGGREGATED DATA

1 IntroductionWe consider following nonlinear regression model:where y = (yi, y25..., yn)" is an n x 1 response vector with expectationwhere pi(0) = f(xi, 0), i = 1, 2,... 5 n; 0 = (91, 92,... I or)" is a p x I vector of unknown parameters, 0 E O C Re; fi is a q x 1 desigll variable, fi E X, X C Rq, i = 1, 2,... t n; f(., .) is a knownfunction, its field of definition is X x O; V(P(0)) is a positive definite matrix for all 0 E O.Let Y be the n-dimensional sample space. Suppose that on …     

SOME ASYMPTOTIC INFERENCE IN QUASI-LIKELIHOOD NONLINEAR MODELS:A GEOMETRIC APPROACH

§ 1　IntroductionIt is well known that quasi-likelihood models introduced by Wedderburn[1 ] greatlywiden the scope of generalized linear models by using a much weaker assumption in whichonly the firstand second moments ofresponse vector Yare needed to replace the full distri-butional assumption about Y in the models.It has drawn considerable attention in recentliterature(e.g.see[2～ 6] and so on) .However,little work has been done on the issuefrom a geometric viewpoint.The purpose of this p…     

ESTIMATING A STOCHASTIC MODEL OF POPULATION DYNAMICS WITH AN APPLICATION TO KANGAROOS

In this study, we derive stochastic models of population dynamics and devise a new method of estimating the models. The models allow growth and harvest to be nonlinear functions of stochastic processes and the error terms to be nonlinear and heteroskedastic. Ordinary least-squares estimates would be biased and inefficient and generalized least-squares estimates cannot be calculated. Therefore, we implement nonlinear maximum likelihood methods to find unbiased and efficient estimates of parameters. The method is applied to the population dynamics of kangaroos in South Australia. Aerial survey data of kangaroo numbers are combined with harvest, effort and rainfall data to estimate the growth and harvest functions and the variances of the stochastic processes which drive the system. Results suggest that growth and harvest should be modeled as functions of stochastic processes and that observations on kangaroo numbers are critical for estimating population dynamics. The results also indicate that the estimation method works well and is a viable alternative to ARIMA and GARCH models, particularly for small data sets.     

A random model approach for the LASSO

The least absolute selection and shrinkage operator (LASSO) is a method of estimation for linear models similar to ridge regression. It shrinks the effect estimates, potentially shrinking some to be identically zero. The amount of shrinkage is governed by a single parameter. Using a random model formulation of the LASSO, this parameter can be specified as the ratio of dispersion parameters. These parameters are estimated using an approximation to the marginal likelihood of the observed data. The observed score equations from the approximation are biased and hence are adjusted by subtracting an empirical estimate of the expected value. After estimation, the model effects can be tested (via simulation) as the distribution of the observed data given that all model effects are zero is known. Two related simulation studies are presented that show that dispersion parameter estimation results in effect estimates that are competitive with other estimation methods (including other LASSO methods).     

A Class of Linear Biased Estimators of Regression ParameterMatrix in the Growth Curve Model

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Quasi profile and directed likelihoods from estimating functions

Frequently, corresponding to a given estimating equation it would be desirable to have a scalar combinant having parametric derivative equal to the estimating function since such a combinant may serve as a quasi log likelihood. In general this cannot be achieved but it is nevertheless possible to define a quasi profile log likelihood and also a quasi directed likelihood, for an arbitrary one-dimensional parameter of interest and with the standard kind of distributional limit behaviour.     

On Hsu's theorem in multivariate regression

The paper deals with optimal quadratic unbiased estimation of the unknown dispersion matrix in multivariate regression models without assuming normality of the errors. We show that Hsu's theorem for univariate regression models continues to multivariate models with no additional assumptions. Furthermore optimal quadratic plus linear estimating functions for regression coefficients are considered, and we investigate whether the ordinary linear estimates are the best. This leads to a new theorem which is similar to that of Hsu.     

Quasi-Profile Log Likelihoods for Unbiased Estimating Functions

This paper presents a new quasi-profile loglikelihood with the standard kind of distributional limit behaviour, for inference about an arbitrary one-dimensional parameter of interest, based on unbiased estimating functions. The new function is obtained by requiring the corresponding quasi-profile score function to have bias and information bias of order O(1). We illustrate the use of the proposed pseudo-likelihood with an application to robust inference in linear models.     

An adjusted maximum likelihood method for solving small area estimation problems

For the well-known Fay-Herriot small area model, standard variance component estimation methods frequently produce zero estimates of the strictly positive model variance. As a consequence, an empirical best linear unbiased predictor of a small area mean, commonly used in small area estimation, could reduce to a simple regression estimator, which typically has an overshrinking problem. We propose an adjusted maximum likelihood estimator of the model variance that maximizes an adjusted likelihood defined as a product of the model variance and a standard likelihood (e.g., a profile or residual likelihood) function. The adjustment factor was suggested earlier by Carl Morris in the context of approximating a hierarchical Bayes solution where the hyperparameters, including the model variance, are assumed to follow a prior distribution. Interestingly, the proposed adjustment does not affect the mean squared error property of the model variance estimator or the corresponding empirical best linear unbiased predictors of the small area means in a higher order asymptotic sense. However, as demonstrated in our simulation study, the proposed adjustment has a considerable advantage in small sample inference, especially in estimating the shrinkage parameters and in constructing the parametric bootstrap prediction intervals of the small area means, which require the use of a strictly positive consistent model variance estimate.