基于最大惩罚似然的高斯混合模型无监督分类研究

本文提出了一个基于高斯混合模型的无监督分类算法. 考虑到利用EM算法求解高斯混合模型的参数参数估计问题容易陷入局部最优解, 我们引入逆Wishart分布来代替传统的Jeffery先验. 几个实验数据的结果表明, 采用该方法估计无监督分类的成分数, 无论是估计的正确率, 还是运算速度, 都有较大提高.     

Restricted Maximum Likelihood Estimates in Finite Mixture Models

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On Maximum Likelihood Estimation for Gaussian Spatial Autoregression Models

The article presents a central limit theorem for the maximum likelihood estimator of a vector-valued parameter in a linear spatial stochastic difference equation with Gaussian white noise right side. The result is compared to the known limit theorems derived for the approximate likelihood e.g. by Whittle (1954, Biometrika, 41, 434-439), Guyon (1982, Biometrika, 69, 95-105) and Rosenblatt (1985, Stationary Sequences and Random Fields, Birkhäuser, Boston) and to the asymptotic properties of the quasi-likelihood studied by Heyde and Gay (1989, Stochastic Process. Appl., 31, 223-236; 1993, Stochastic Process. Appl., 45, 169-182). Application of the theory is demonstrated on several classes of models including the one considered by Niu (1995, J. Multivariate Anal., 55, 82-104).     

A Cautionary Note on Likelihood Ratio Tests in Mixture Models

We show that iterative methods for maximizing the likelihood in a mixture of exponentials model depend strongly on their particular implementation. Different starting strategies and stopping rules yield completely different estimators of the parameters. This is demonstrated for the likelihood ratio test of homogeneity against two-component exponential mixtures, when the test statistic is calculated by the EM algorithm.     

Generalized Moment Theory and Bayesian Robustness Analysis for Hierarchical Mixture Models

In applications of Bayesian analysis one problem that arises is the evaluation of the sensitivity, or robustness, of the adopted inferential procedure with respect to the components of the formulated statistical model. In particular, it is of interest to study robustness with respect to the prior, when this latter cannot be uniquely elicitated, but a whole class Γ of probability measures, agreeing with the available information, can be identified. In this situation, the analysis of robustness consists of finding the extrema of posterior functionals under Γ. In this paper, we provide a theoretical framework for the treatment of a global robustness problem in the context of hierarchical mixture modeling, where the mixing distribution is a random probability whose law belongs to a generalized moment class Γ. Under suitable conditions on the functions describing the problem, the solution of this latter coincides with the solution of a linear semi-infinite programming problem.     

Two New Mixture Models Related to the Inverse Gaussian Distribution

This article presents a new family of logarithmic distributions to be called the sinh mixture inverse Gaussian model and its associated life distribution referred as the extended mixture inverse Gaussian model. Specifically, the density, distribution function, and moments are developed for the sinh mixture inverse Gaussian distribution. Next, the extended mixture inverse Gaussian distribution is characterized. A graphical analysis of the densities of the new models is also provided. In addition, a lifetime analysis is presented for the extended mixture inverse Gaussian distribution. Finally, an example with a real data set is given to illustrate the methodology, which indicates that the new models result in a better fit to the data than some other well-known distributions.     

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.     

非线性半参数回归模型的最大经验似然估计

对于非线性半参数回归模型的估计问题,利用经验似然方法,给出了回归系数,光滑函数以及误差方差的最大经验似然估计.在一定条件下证明了所得估计量的渐近正态性和相合性.     

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。     

Bayesian and Maximum Likelihood Estimation for Gaussian Processes on an Incomplete Lattice

This article proposes a new approach for Bayesian and maximum likelihood parameter estimation for stationary Gaussian processes observed on a large lattice with missing values. We propose a Markov chain Monte Carlo approach for Bayesian inference, and a Monte Carlo expectation-maximization algorithm for maximum likelihood inference. Our approach uses data augmentation and circulant embedding of the covariance matrix, and provides likelihood-based inference for the parameters and the missing data. Using simulated data and an application to satellite sea surface temperatures in the Pacific Ocean, we show that our method provides accurate inference on lattices of sizes up to 512 × 512, and is competitive with two popular methods: composite likelihood and spectral approximations.     

Empirical Likelihood in Generalized Linear Models with Working Covariance Matrix

Empirical likelihood in generalized linear models with multivariate responses and working covariance matrix is discussed. Under the weakest assumption on eigenvalues of Fisher’s information matrix and some other regular conditions, we prove that the non-parametric Wilk’s property still holds, that is, the empirical log-likelihood ratio at the true parameter values converges to the standard chi-square distribution. Numerical simulations are given to verify our theoretical result.     

重复测量试验模型参数似然比检验及其功效分析

本文给出了在重复测量试验模型下, 当受试对象观测向量的协方差矩阵$\Sigma$为复合对称阵时,参数的似然比检验统计量; 给出该检验在原假设下的渐近零分布和在备择假设下的渐近非零分布;并就其功效进行了分析.     

半参数回归模型小波估计的矩相合性

用小波方法,考虑半参数回归模型y_i=X_i~Tβ+g(t_i)+ε_i(1≤i≤n),其中β∈R~d为未知参数,g(t)为[0,1]上未知的Borel可测函数,X_i为R~d上的随机设计,随机误差{ε_i}为鞅差序列,{t_i}为[0,1]上的常数序列.得到参数及非参数的小波估计量的q-阶矩相合性.     

泊松回归模型中协变量含误差的经验似然推断

在模型的协变量含有测量误差的情况下,考虑一类泊松回归模型的统计推断问题.通过巧妙地构造辅助随机向量,提出一个工具变量类型的经验似然统计推断方法.证明构造的经验对数似然比函数渐近服从标准卡方分布,进而给出了回归系数的置信区间.所提出的估计方法可以有效地消除测量误差对估计精度的影响,并且具有较好的有限样本性质.     

A Connection between Time Domain Model Order Reduction and Moment Matching

We investigate the time domain model order reduction (MOR) framework using general orthogonal polynomials by Jiang and Chen [4] and extend their idea by exploiting the structure of the corresponding linear system of equations. Identifying an equivalent Sylvester equation we show a connection to a rational Krylov subspace, and thus moment matching. This theoretical link between the MOR techniques is illustrated by one numerical example. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

核实数据下非线性半参数EV模型的经验似然推断

考虑带有协变量误差的非线性半参数模型,借助于核实数据,本文构造了未知参数的三种经验对数似然比统计量,证明了所提出的统计量具有渐近X2分布,此结果可以用来构造未知参数的置信域．另外,本文也构造了未知参数的最小二乘估计量,并证明了它的渐近性质．仅就置信域及其覆盖概率的大小方面,通过模拟研究比较了经验似然方法与最小二乘法的优劣．     

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The additive model is a more flexible nonparametric statistical model which allows a data-analytic transform of the covariates.When the number of covariates is big and grows exponentially with the sample size the urgent issue is to reduce dimensionality from high to a moderate scale. In this paper, we propose and investigate marginal empirical likelihood screening methods in ultra-high dimensional additive models. The proposed nonparametric screening method selects variables by ranking a measure of the marginal empirical likelihood ratio evaluated at zero to differentiate contributions of each covariate given to a response variable. We show that, under some mild technical conditions, the proposed marginal empirical likelihood screening methods have a sure screening property and the extent to which the dimensionality can be reduced is also explicitly quantified. We also propose a data-driven thresholding and an iterative marginal empirical likelihood methods to enhance the finite sample performance for fitting sparse additive models. Simulation results and real data analysis demonstrate the proposed methods work competitively and performs better than competitive methods in error of a heteroscedastic case.     

Exponential Mixture Models with Long-Term Survivors and Covariates

Suppose a population contains individuals who may be subject to failure with exponentially distributed failure times, or else are "immune" to failure. We do not know which individuals are immune but we can infer their presence in a data set if many of the largest failure times are censored. We also have explanatory vectors containing covariate information on each individual. Models for data with such immune or "cured" individuals are of great interest in medical and criminological statistics, for example. In this paper we provide sufficient conditions for the existence, consistency, and asymptotic normality of maximum likelihood estimators for the parameters in a useful parameterization of these models. The theory is then applied to derive the asymptotic properties of the likelihood ratio test for a difference between immune proportions in a "one-way" classification. A procedure for testing the "boundary" hypothesis, that there are in fact no immunes present in data with a one-way classification, is also discussed.     

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.