有限混合模型有限制Log极大似然比统计量的极限分布

有限混合模型的Log极大似然比统计量极限分布不是平常x2分布,1985年已为Hartigan指出.在这篇文章我们限制了混合比大于一正数下,讨论了两个含单个未知参数混合模型的Log极大似然比统计量的极限分布,它是零与x2分布的混合分布.     

Likelihood Ratio Statistic for Exponential Mixtures

Let f ₀(x) be the exponential density and f (x) the translation model. Let (X _i) _i=1,n be i.i.d. random variables, with density g. We test that g is f ₀ against g is a simple mixture, using the LRT statistic. We prove that the LRT diverges to infinity with probability 1/2 and it is equal to 0 with probability 1/2. Therefore, the classical likelihood limiting theory does not hold.     

A Note on the Estimation of Semiparametric Two-Sample Density Ratio Models

In this paper,a semiparametric two-sample density ratio model is considered and the empirical likelihood method is applied to obtain the parameters estimation.A commonly occurring problem in computing is that the empirical likelihood function may be a concaveconvex function.Here a simple Lagrange saddle point algorithm is presented for computing the saddle point of the empirical likelihood function when the Lagrange multiplier has no explicit solution.So we can obtain the maximum empirical likelihood estimation (MELE) of parameters.Monte Carlo simulations are presented to illustrate the Lagrange saddle point algorithm.     

两个未知均值方差混合模型有限制下对数极大似然比的极限分布

本文讨论了检验样本是来自一个正态总体还是两个未知均值和方差的正态的混合分布,采用对数极大似然比的检验,如果不加限制,Ｈａｒｔｉｎｇａｎｍ曾指出不是寻找的、Ｘ＾２分布,我们在混合的中了一点后得到了其极限分布产工给出了分位点数值表。     

离子通道的混合密度参数估计与状态判别

本文针对多电导水平离子通道的由多个正态分布加权组成的混合分布特点,用EM迭代算法对混合分布中的参数进行极大似然估计,并在此基础上,利用混合分布中最可能的成分判断通道状态,从而还原通道潜在信号,克服了离子通道分析软件PCLAMP中参数估计与状态还原的缺陷。     

Maximum likelihood estimation in the multi-path change-point problem

Maximum likelihood estimators of the parameters of the distributions before and after the change and the distribution of the time to change in the multi-path change-point problem are derived and shown to be consistent. The maximization of the likelihood can be carried out by using either the EM algorithm or results from mixture distributions. In fact, these two approaches give equivalent algorithms. Simulations to evaluate the performance of the maximum likelihood estimators under practical conditions, and two examples using data on highway fatalities in the United States, and on the health effects of urea formaldehyde foam insulation, are also provided.This work was supported in part by the Natural Science and Engineering Council of Canada, and the Fonds pour la Formation de chercheurs et l'aide à la Recherche Gouvernment du Québec.Lawrence Joseph is also a member of the Department of Epidemiology and Biostatistics of McGill University.     

偏t正态数据下混合线性联合位置与尺度模型的参数估计

偏t正态分布是分析尖峰,厚尾数据的重要统计工具之一.研究提出了偏t正态数据下混合线性联合位置与尺度模型,通过EM算法和Newton-Raphson方法研究了该模型参数的极大似然估计.并通过随机模拟试验验证了所提出方法的有效性.最后,结合实际数据验证了该模型和方法具有实用性和可行性.     

非线性联立方程模型的充分信息最大加权似然估计及其性质

提出非线性联立方程模型的充分信息最大加权似然估计并得到其一致性和渐近正态性的大样本性质 .     

Clustering Based on a Multilayer Mixture Model

In model-based clustering, the density of each cluster is usually assumed to be a certain basic parametric distribution, for example, the normal distribution. In practice, it is often difficult to decide which parametric distribution is suitable to characterize a cluster, especially for multivariate data. Moreover, the densities of individual clusters may be multimodal themselves, and therefore cannot be accurately modeled by basic parametric distributions. This article explores a clustering approach that models each cluster by a mixture of normals. The resulting overall model is a multilayer mixture of normals. Algorithms to estimate the model and perform clustering are developed based on the classification maximum likelihood (CML) and mixture maximum likelihood (MML) criteria. BIC and ICL-BIC are examined for choosing the number of normal components per cluster. Experiments on both simulated and real data are presented.     

竞争失效产品加速寿命试验的参数估计

讨论了指数分布场合竞争失效产品加速寿命试验的参数估计,对常用极大似然估计作了一些改进,从而使改进后的参数估计在均方误差意义下更优.     

基于Dirichlet分布有限混合模型的Bayes聚类

本文基于Dirichlet分布有限混合模型,提出了一种用于成分数据的Bayes聚类方法.采用EM算法获得模型参数的估计,用BIC准则确定类数,用类似于Bayes判别的方法对各观测分类.推导了计算公式,编写出程序.模拟研究结果表明,本文提出的方法有较好的聚类效果.     

方差未知时两样本正态混合模型齐-性的修正似然比检验

本文讨论了方差未知时检验两样本正态混合模型齐一性的修正似然比统计量的极限性质,证明了原假设下修正似然比统计量的渐近分布为自由度为1的卡方分布.     

混合双重广义线性模型的参数估计

在实际应用中,不同类别的数据统计特性存在差异,所以对异质总体的研究非常有必要.基于总体一,二阶矩存在,利用双重广义线性模型对异质总体的不同子类数据的均值和散度同时建模,研究提出了混合双重广义线性模型.然后,利用EM算法构造了模型参数的最大扩展拟似然估计和最大伪似然估计.最后,通过随机模拟和实例研究,结果表明模型和方法的有效性和有用性.     

竞争风险混合模型的参数估计与检验

本文在独立同分布I型区间删失情形下,研究了竞争风险混合模型中当参数真值是内点时,参数极大似然估计的性质,获得了其强相合性和渐近正态性.在较为宽松的条件下,给出了竞争风险混合模型参数序关系假设检验的检验方法,同时得到了似然比检验统计量及其在零假设下的渐近分布为加权x~2分布,并给出了—个例子并进行了功效比较.     

Analysis of two-sample censored data using a semiparametric mixture model

In this article we study a semiparametric mixture model for the two-sample problem with right censored data. The model implies that the densities for the continuous outcomes are related by a parametric tilt but otherwise unspecified. It provides a useful alternative to the Cox （1972） proportional hazards model for the comparison of treatments based on right censored survival data. We propose an iterative algorithm for the semiparametric maximum likelihood estimates of the parametric and nonparametric components of the model. The performance of the proposed method is studied using simulation. We illustrate our method in an application to melanoma.     

An EM Algorithm for Batch Markovian Arrival Processes and its Comparison to a Simpler Estimation Procedure

Although the concept of Batch Markovian Arrival Processes (BMAPs) has gained widespread use in stochastic modelling of communication systems and other application areas, there are few statistical methods of parameter estimation proposed yet. However, in order to practically use BMAPs for modelling, statistical model fitting from empirical time series is an essential task. The present paper contains a specification of the classical EM algorithm for MAPs and BMAPs as well as a performance comparison to the computationally simpler estimation procedure recently proposed by Breuer and Gilbert. Furthermore, it is shown how to adapt the latter to become an estimator for hidden Markov models.     

Types of likelihood maxima in mixture models and their implication on the performance of tests

In two-component mixtures of exponential distributions, different strategies for starting the likelihood maximization algorithm converge to different types of maxima. The power of an LR test of homogeneity against such a mixture strongly depends on the considered strategy, and global maximization need not result in the largest power. An explanation is given on basis of a systematic investigation of the likelihood function in a large number of simulations, using a variety of diagnostic tools. Thereby, we also gain a deeper insight into the properties of the samples that generate particular types of solutions of the likelihood equation. In particular, “spurious solutions” often occur; these are mainly responsible for the fact that global maximization may not result in a statistically meaningful estimator. Removing the smallest elements of a sample may drastically increase the power of previously inferior strategies. This research has been supported by a grant from the Deutsche Forschungsgemeinschaft.     

Large Sample Properties of Mixture Models with Covariates for Competing Risks

We study the large-sample properties of a class of parametric mixture models with covariates for competing risks. The models allow general distributions for the survival times and incorporate the idea of long-term survivors. Asymptotic results are obtained under a commonly assumed independent censoring mechanism and some modest regularity conditions on the survival distributions. The existence, consistency, and asymptotic normality of maximum likelihood estimators for the parameters of the model are rigorously derived under general sufficient conditions. Specific conditions for particular models can be derived from the general conditions for ready check. In addition, a likelihood-ratio statistic is proposed to test various hypotheses of practical interest, and its asymptotic distribution is provided.     

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.     

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The hybrid censoring scheme is a mixture of type-I andtype-II censoring schemes. It is a popular censoring scheme in the literatureof life data analysis. Mixed exponential distribution (MED) models is a classof favorable models in reliability statistics. Nevertheless, there is no muchdiscussion to focus on parameters estimation for MED models with hybridcensored samples. We will address this problem in this paper. The EM(Expectation-Maximization) algorithm is employed to derive the closed form ofthe maximum likelihood estimators (MLEs). Finally, Monte Carlo simulations anda real-world data analysis are conducted to illustrate the proposed method.