AR(p)模型中的变点分析

本文分别用极大似然法和Bayes方法研究了AR(p)模型中的变点问题.在数据矩阵不一定满秩的条件下,利用Moore-Penrose广义逆给出了模型参数的极大似然估计的统一表达式和变点位置的估计式.在假定自回归系数的先验分布服从多元正态,方差服从逆Γ分布的条件下,用Bayes方法给出了变点位置估计的显示表达式以及模型参数的Bayes估计.     

带Gauss型误差的GMANOVA-MANOVA模型中未知参数的精确置信域

对于带Gauss型误差的GMANOVA-MANOVA模型,在均匀协方差结构下,求出了其中未知参数的极大似然估计及其均值和方差,并依据极大似然估计构造了未知参数的精确置信域.     

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.     

序约束下ARCH(0,2)模型参数估计与检验

本文研究了平稳ARCH（0，2）模型未知参数α的极大似然估计及有序约束时α的极大似然估计的渐近性质，给出了参数序关系（α1≥α2）的检验方法，并得出了似然比检验统计量的渐近分布。用二次规划的算法，给出求各种情况下参数α的极大似然估计的数值算法。     

半参数回归模型拟极大似然估计的渐近分布

用拟极大似然估计方法研究了误差为AR(1)时间序列的半参数回归模型,得到了参数及非参数的拟极大似然估计量,并研究了它们的渐近分布.     

基于M估计的指数相关非线性混合效应模型的齐性检验(英文)

方差和相关系数的齐性是纵向数据分析中常用假设之一,然而,这些假设未必合适.本文主要研究的是具有指数相关结构的纵向数据非线性混合效应模型,首先将Huber函数引入模型的对数似然函数中,利用Fisher得分迭代法得到模型参数的稳健估计(M估计),然后基于M估计对模型的方差和相关系数的齐性进行了Score检验,并给出了检验统计量的Monte-Carlo模拟结果.最后用一个实例说明了本文的方法.     

平衡随机模型中方差分量的非负估计

众所周知, 对于平衡随机模型, 方差分量的方差分析估计为一致最小方差无偏估计. 本文基于方差分量的方差分析估计, 构造了一个二次不变估计类, 它包含了一些常用重要估计. 证明了该估计类在一定条件下在均方误差意义下一致优于方差分析估计, 并在此估计类基础上, 给出了方差分量的两种非负估计, 它们在均方误差意义下分别一致优于方差分析估计和限制极大似然估计, 且有显式解、容易计算.     

关于多级评分的考生能力评价模型的探讨

本文对多级评分的考试给出了一个评价考生能力的模型,它作为0-1评分二参数logistio型的推广,并给出了用极大似然法估计能力参数的迭代步骤。     

Cox-Ingersoll-Ross模型的统计推断

本文研究了Cox—Ingersoll—Ross模型的统计推断问题.给出了CIR过程的平稳均值m与平稳方差v的矩估计,并利用m和v给出了CIR过程中尺度参数α与波动率β之间的关系,讨论了参数α的条件矩估计和渐近极大似然估计.并通过数值模拟对条件矩估计,渐近极大似然估计这两种方法作了比较.     

基于经验似然的AR(p)模型的统计诊断

本文基于经验似然方法对AR(p)模型进行统计诊断,文章首先给出p阶自回归模型的广义估计函数并对模型参数进行估计,然后运用数据删失、局部影响分析和伪残差方法对AR(p)模型进行统计诊断,最后通过实证来说明该诊断方法的有效性.     

Improving on the mle of a bounded location parameter for spherical distributions

For the problem of estimating under squared error loss the location parameter of a p-variate spherically symmetric distribution where the location parameter lies in a ball of radius m, a general sufficient condition for an estimator to dominate the maximum likelihood estimator is obtained. Dominance results are then made explicit for the case of a multivariate student distribution with d degrees of freedom and, in particular, we show that the Bayes estimator with respect to a uniform prior on the boundary of the parameter space dominates the maximum likelihood estimator whenever and d?p. The sufficient condition matches the one obtained by Marchand and Perron (Ann. Statist. 29 (2001) 1078) in the normal case with identity covariance matrix. Furthermore, we derive an explicit class of estimators which, for , dominate the maximum likelihood estimator simultaneously for the normal distribution with identity covariance matrix and for all multivariate student distributions with d degrees of freedom, d?p. Finally, we obtain estimators which dominate the maximum likelihood estimator simultaneously for all distributions in the subclass of scale mixtures of normals for which the scaling random variable is bounded below by some positive constant with probability one.     

Existence and consistency of the maximum likelihood estimator for the extreme value index

The paper is about the asymptotic properties of the maximum likelihood estimator for the extreme value index. Under the second order condition, Drees et al. [H. Drees, A. Ferreira, L. de Haan, On maximum likelihood estimation of the extreme value index, Ann. Appl. Probab. 14 (2004) 1179-1201] proved asymptotic normality for any solution of the likelihood equations (with shape parameter γ>−1/2) that is not too far off the real value. But they did not prove that there is a solution of the equations satisfying the restrictions.In this paper, the existence is proved, even for γ>−1. The proof just uses the domain of attraction condition (first order condition), not the second order condition. It is also proved that the estimator is consistent. When the second order condition is valid, following the current proof, the existence of a solution satisfying the restrictions in the above-cited reference is a direct consequence.     

A Comparison of Restricted and Unrestricted Estimators in Estimating Linear Functions of Ordered Scale Parameters of Two Gamma Distributions

The problem of estimating linear functions of ordered scale parameters of two Gamma distributions is considered. A necessary and sufficient condition on the ratio of two coefficients is given for the maximum likelihood estimator (MLE) to dominate the crude unbiased estimator (UE) in terms of mean square error. A modified MLE which satisfies the restriction is also suggested, and a necessary and sufficient condition is also given for it to dominate the admissible estimator based solely on one sample. The estimation of linear functions of variances in two sample problem and also of variance components in a one-way random effect model is mentioned.     

Likelihood estimation of the extremal index

The article develops the approach of Ferro and Segers (J.R. Stat. Soc., Ser. B 65:545, 2003) to the estimation of the extremal index, and proposes the use of a new variable decreasing the bias of the likelihood based on the point process character of the exceedances. Two estimators are discussed: a maximum likelihood estimator and an iterative least squares estimator based on the normalized gaps between clusters. The first provides a flexible tool for use with smoothing methods. A diagnostic is given for condition , under which maximum likelihood is valid. The performance of the new estimators were tested by extensive simulations. An application to the Central England temperature series demonstrates the use of the maximum likelihood estimator together with smoothing methods.      

Parametrization Invariance with Respect to Second Order Admissibility Under Mean Squared Error

Our main concern is about second order admissibility under mean squared error. A sufficient condition and a necessary condition for a modified maximum likelihood estimator to be second order admissible regardless of parametrization are obtained. In addition, some procedures for characterizing such estimators are provided.     

套重复测量模型的充分性和估计

当每一个体有相同的子个体,并且每一子个体的处理水平是成对的时候,我们使用套重复测量模型.令Yi=(Yilll,…Yimrc)′是第i个个体的观测向量.假设Yi为相互独立的正态分布,均值为μi,协方差阵为∑＞0.假设可简化为所有测量值的方差为σ2;相同个体的不同子个体之间的成对测量值之间的关系如下(1)不同列不同行的观测值;(2)相同列不同行的测量值;(3)相同行不同列的测量值,它们的协方差分别为ρ2σ2,ρ3σ2,ρ4σ2.我们假设试验是给定的,用坐标自由(coordinate-free)的方法研究了套重复测量模型的完备充分统计量,最小方差无偏估计(MVUE)和极大似然估计(MLE).     

On the comparison of the pre-test and shrinkage phi-divergence test estimators for the symmetry model of categorical data

The estimation problem of the parameters in a symmetry model for categorical data has been considered for many authors in the statistical literature (for example, Bowker (1948) [1], Ireland et al. (1969) [2], Quade and Salama (1975) [3], Cressie and Read (1988) [4], Menéndez et al. (2005) [5]) without using uncertain prior information. It is well known that many new and interesting estimators, using uncertain prior information, have been studied by a host of researchers in different statistical models, and many papers have been published on this topic (see Saleh (2006) [9] and references therein). In this paper, we consider the symmetry model of categorical data and we study, for the first time, some new estimators when non-sample information about the symmetry of the probabilities is considered. The decision to use a “restricted” estimator or an “unrestricted” estimator is based on the outcome of a preliminary test, and then a shrinkage technique is used. It is interesting to note that we present a unified study in the sense that we consider not only the maximum likelihood estimator and likelihood ratio test or chi-square test statistic but we consider minimum phi-divergence estimators and phi-divergence test statistics. Families of minimum phi-divergence estimators and phi-divergence test statistics are wide classes of estimators and test statistics that contain as a particular case the maximum likelihood estimator, likelihood ratio test and chi-square test statistic. In an asymptotic set-up, the biases and the risk under the squared loss function for the proposed estimators are derived and compared. A numerical example clarifies the content of the paper.     

Full likelihood inferences in the Cox model: an empirical likelihood approach

For the regression parameter β ₀ in the Cox model, there have been several estimators constructed based on various types of approximated likelihood, but none of them has demonstrated small-sample advantage over Cox’s partial likelihood estimator. In this article, we derive the full likelihood function for (β ₀, F ₀), where F ₀ is the baseline distribution in the Cox model. Using the empirical likelihood parameterization, we explicitly profile out nuisance parameter F ₀ to obtain the full-profile likelihood function for β ₀ and the maximum likelihood estimator (MLE) for (β ₀, F ₀). The relation between the MLE and Cox’s partial likelihood estimator for β ₀ is made clear by showing that Taylor’s expansion gives Cox’s partial likelihood estimating function as the leading term of the full-profile likelihood estimating function. We show that the log full-likelihood ratio has an asymptotic chi-squared distribution, while the simulation studies indicate that for small or moderate sample sizes, the MLE performs favorably over Cox’s partial likelihood estimator. In a real dataset example, our full likelihood ratio test and Cox’s partial likelihood ratio test lead to statistically different conclusions.     

The extent of the maximum likelihood estimator for the extreme value index

In extreme value analysis, staring from Smith (1987) [1], the maximum likelihood procedure is applied in estimating the shape parameter of tails—the extreme value index γ. For its theoretical properties, Zhou (2009) [12] proved that the maximum likelihood estimator eventually exists and is consistent for γ>−1 under the first order condition. The combination of Zhou (2009) [12] and Drees et al (2004) [11] provides the asymptotic normality under the second order condition for γ>−1/2. This paper proves the asymptotic normality for −1<γ≤−1/2 and the non-consistency for γ<−1. These results close the discussion on the theoretical properties of the maximum likelihood estimator.     

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.