线性模型误差方差的经验似然估计

本文应用经验似然方法得到了线性模型误差方差的一类新的估计,证明了估计的渐近分布为正态分布且渐近方差不超过常用的误差方差估计的渐近方差,同时给出了渐近方差的显式表达.     

广义线性回归极大似然估计的强相合性

设有该文第1节所描述的广义线性回归模型,以$\underline{\lambda}_n$和$\overline{\lambda}_n$分别记$\sum\limits_{i=1}^{n}Z_iZ_i^{\prime}$的最小和最大特征根,$\hat{\beta}_n$记$\beta_0$的极大似然估计.在文献[1]中,当\{$Z_i,i\ge1$\}有界时得到$\hat{\beta}_n$强相合的充分条件,在自然联系和非自然联系下分别为$\underline{\lambda}_n\rightarrow\infty$, $(\overline{\lambda}_n)^{1/2+\delta}=O(\underline{\lambda}_n)$（对某$\delta>0$)以及$\underline{\lambda}_n\rightarrow\infty$, $\overline{\lambda}_n=O(\underline{\lambda}_n)$.作者将后一结果改进为只要求$(\overline{\lambda}_n)^{1/2+\delta}=O(\underline{\lambda}_n)$,从而与自然联系情况下的条件达到一致.     

截尾线性回归模型参数极大似然估计的存在性和唯一性

考虑带有截尾数据的线性回归模型,在较为-般的截尾数据情形下,本文给出了其参数极大似然估计(MLE)存在且唯一的充分必要条件,且对MLE不存在的样本数据集Q的描述定义更为准确.     

非正则位置参数模型中的拟极大似然估计

当分布密度的形式未知时，参数的极大似然估计没有明确的解析表达式，也不能通过设计算法由计算机运算得到。本文我们将从该分布中抽取的样本当作是来自另一个形式已知的分布密度的样本，该已知分布密度的选取依赖于未知的分布密度，但是具有与未知分布相似的边界性质。基于这两个分布族，我们提出了拟极大似然估计的概念，同时，对这种拟极大似然估计的渐近性质进行了讨论。结果表明拟极大拟然估计与极大似然估计有关相同的渐近性质，并且由于拟极大似然估计的获得不依赖于未知分布密度的形式，只与一已知的分布密度有关，使得通过计算机可以实现对其的求解。     

ARMA模型变化点的极大似然估计

设W_1,…W_(n-1),W_n,…,W_m是对系统S的无间断等时间间隔的K维观测向量,样本W_1,…,W_(n-1)和样本W_n,…,W_m相互独立且分别来自两个不同的ARMA模型:     

部分线性模型参数极大似然估计的收敛速度

针对部分线性模型, 在其随机误差的分布函数属于刻度族, 刻度参数未知, 并且响应变量的观测值为区间删失数据的情形下, 讨论了其Sieve极大似然估计的强相合性和弱收敛速度.     

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.     

多项Probit模型参数的极大似然估计

本文考虑多项probit模型中参数的极大似然估计(MLE)的存在性.在协方差阵已知和均匀结构两种情况下,给出MLE存在的充要条件.     

保序回归与最大似然估计

约束条件下的统计推断巳成为统计分析中一个重要的研究领域,而保序回归的研究又是其中之关键。本文通过一个实例引导出统计模型,比较系统地总结了保序回归的性质、求解方法,以及与最大似然估计之间的关系。本文还把问题扩展到多维保序回归和广义保序回归。     

再论ARMA模型参数极大似然估计的收敛速度

本文给出了ＡＲＭＡ模型参数的极大似然估计和最小平方和估计的强收敛速度。     

半参数变系数异方差部分线性模型下的经验似然

Consider the semiparametric varying-coefficient heteroscedastic partially linear model Y i = Xτiβ + Zτiα(Ti) + σiei,1 ≤ i ≤ n,where σ 2 i = f(Ui),β is a p × 1 column vector of unknown parameter,(Xi,Zi,Ti,Ui) are random design points,Y i are the response variables,α(·) is a q-dimensional vector of unknown functions,e i are random errors.For both cases that f(·) is known and unknown,we propose the empirical log-likelihood ratio statistics for the parameter β.For each case,a nonparametric version of Wilks’ theorem is derived.The results are then used to construct confidence regions of the parameter.Simulation studies are carried out to assess the performance of the empirical likelihood method.     

Stable Computation of Maximum Likelihood Estimates in Identity Link Poisson Regression

Identity link Poisson regression is useful when the mean of a count variable depends additively on a collection of predictor variables. It is particularly important in epidemiology, for modeling absolute differences in disease incidence rates as a function of covariates. A complication of such models is that standard computational methods for maximum likelihood estimation can be numerically unstable due to the nonnegativity constraints on the Poisson means. Here we present a straightforward and flexible method that provides stable maximization of the likelihood function over the constrained parameter space. This is achieved by conducting a sequence of maximizations within subsets of the parameter space, after which the global maximum is identified from among the subset maxima. The method adapts and extends EM algorithms that are useful in specialized applications involving Poisson deconvolution, but which do not apply in more general regression contexts. As well as allowing categorical and continuous covariates, the method has the flexibility to accommodate covariates with an unspecified isotonic form. Its computational reliability makes it particularly useful in bootstrap analyses, which may require stable convergence for thousands of implementations. Computations are illustrated using epidemiological data on occupational mortality, and biological data on crab population counts. This article has supplementary material online.     

Degeneracy in Heteroscedastic Regression Models

The maximum likelihood estimation in a regression model with heteroscedastic errors is considered. When the design matrices in the model are inappropriately specified, the maximum likelihood estimates of the variances of certain observations are found to be zero irrespective of the observed values, resulting in degeneracy. Necessary and sufficient conditions for degeneracy are given and used for its avoidance.     

缺失数据下线性模型中回归参数的经验似然置信区域

在缺失样本下,构造了线性模型中参数的调整的经验似然置信域,数值模拟表明调整的经验似然置信域有较好的覆盖率和精度.     

带一个插值点的回归模型的参数分析

一般的回归模型中认为所有的数据点的重要程度是相同的,但有的实际问题中可能由于种种原因,其中有某个数据特别重要,针对这种情况,提出一种带一个插值点的回归模型,并得到这种回归模型三个参数的最大似然估计.     

WEIBULL分布步进应力加速寿命试验损伤失效率模型参数的近似极大似然估计和逆矩估计

Bhattacharyya和Soejoeti(1980)对步进应力加速寿命试验提出损伤失效率模型(TFR模型)．本针对TFR模型，对两参数Weibull分布，在步进应力加速试验下给出了参数的近似极大似然估计和逆矩估计，并通过Montr-Carlo模拟考察了估计的精度，比较了各估计的优劣。     

Efficient Algorithm for Computing Maximum Likelihood Estimates in Linear Transformation Models

Linear transformation models, which have been extensively studied in survival analysis, include the two special cases: the proportional hazards model and the proportional odds model. Nonparametric maximum likelihood estimation is usually used to derive the efficient estimators. However, due to the large number of nuisance parameters, calculation of the nonparametric maximum likelihood estimator is difficult in practice, except for the proportional hazards model. We propose an efficient algorithm for computing the maximum likelihood estimates, where the dimensionality of the parameter space is dramatically reduced so that only a finite number of equations need to be solved. Moreover, the asymptotic variance is automatically estimated in the computing procedure. Extensive simulation studies indicate that the proposed algorithm works very well for linear transformation models. A real example is presented for an illustration of the new methodology.     

多周期Probit模型中MLE的存在性

本文我们讨论了多周期Probit模型中MLE的存在性问题,给出了当协方差阵已知时,参数的MLE存在的充要条件;当协方差阵未知但具有序列结构时,参数的MLE存在的一个必要条件和一个充分条件.