正态分布在不同先验下的Bayes估计及风险比较

本文讨论在均值未知,方差已知的正态分布情况下通过在共轭先验以及Jeffreys先验二种先验下的Bayes估计问题,在平方损失函数下和线性损失函数下Bayes风险的比较.数据计算可以看出,在Jeffreys先验下的Bayes风险要比在共轭先验下的Bayes风险要大,但是当样本量增大时,两者的后验风险越来越靠近.     

A Skew Laplace Distribution on Integers

We propose a discrete version of the skew Laplace distribution. In contrast with the discrete normal distribution, here closed form expressions are available for the probability density function, the distribution function, the characteristic function, the mean, and the variance. We show that this distribution on integers shares many properties of the skew Laplace distribution on the real line, including unimodality, infinite divisibility, closure properties with respect to geometric compounding, and a maximum entropy property. We also discuss statistical issues of estimation under this model.     

Bayesian estimation of regression parameters in elliptical measurement error models

The main object of this paper is to discuss the Bayes estimation of the regression coefficients in the elliptically distributed simple regression model with measurement errors. The posterior distribution for the line parameters is obtained in a closed form, considering the following: the ratio of the error variances is known, informative prior distribution for the error variance, and non-informative prior distributions for the regression coefficients and for the incidental parameters. We proved that the posterior distribution of the regression coefficients has at most two real modes. Situations with a single mode are more likely than those with two modes, especially in large samples. The precision of the modal estimators is studied by deriving the Hessian matrix, which although complicated can be computed numerically. The posterior mean is estimated by using the Gibbs sampling algorithm and approximations by normal distributions. The results are applied to a real data set and connections with results in the literature are reported.     

测量误差模型的自适应LASSO变量选择方法研究

本文研究测量误差模型的自适应LASSO(least absolute shrinkage and selection operator)变量选择和系数估计问题.首先分别给出协变量有测量误差时的线性模型和部分线性模型自适应LASSO参数估计量,在一些正则条件下研究估计量的渐近性质,并且证明选择合适的调整参数,自适应LASSO参数估计量具有oracle性质.其次讨论估计的实现算法及惩罚参数和光滑参数的选择问题.最后通过模拟和一个实际数据分析研究了自适应LASSO变量选择方法的表现,结果表明,变量选择和参数估计效果良好.     

最大似然方法和Bayes方法在结构方程模型分析中的讨论

本文通过模拟研究,讨论了最大似然方法和Bayes方法在分析结构方程模型中的相似点和不同之处。     

位置参数分布族中Fiducial分布与后验分布的关系

本文考虑本质位置参数分布族中,参数的Fiducial分布与后验分布的等同问题．首先讨论了如何给出Fiducial分布,分析结果表明以分布函数形式给出Fiducial分布要比密度函数形式合理,同时,证明了所给的Fiducial分布具有频率性质．然后,研究在参数受到单侧限制时,Fiducial分布与后验分布等同的问题,给出的充要条件是分布族为指数分布族,此时,先验分布是一个广义先验分布,它不能被Lebesgue测度控制．最后,证明了在参数限制在一个有限区间内时,Fiducial分布与任何先验(包括广义先验分布)下的后验分布不等同．     

New prior near-ignorance models on the simplex

The aim of this paper is to derive new near-ignorance models on the probability simplex, which do not directly involve the Dirichlet distribution and, thus, are alternative to the Imprecise Dirichlet Model (IDM). We focus our investigation on a particular class of distributions on the simplex which is known as the class of Normalized Infinitely Divisible (NID) distributions; it includes the Dirichlet distribution as a particular case. For this class it is possible to derive general formulae for prior and posterior predictive inferences, by exploiting the Lévy–Khintchine representation theorem. This allows us to generally characterize the near-ignorance properties of the NID class. After deriving these general properties, we focus our attention on three members of this class. We will show that one of these near-ignorance models satisfies the representation invariance principle and, for a given value of the prior strength, always provides inferences that encompass those of the IDM. The other two models do not satisfy this principle, but their imprecision depends linearly or almost linearly on the number of observed categories; we argue that this is sometimes a desirable property for a predictive model.     

Estimation of autoregressive models with epsilon-skew-normal innovations

A non-Gaussian autoregressive model with epsilon-skew-normal innovations is introduced. Moments and maximum likelihood estimators of the parameters are proposed and their limit distributions are derived. Monte Carlo simulation results are analysed and the model is fitted to a real time series.     

Empirical likelihood estimators for the error distribution in nonparametric regression models

The aim of this paper is to show that existing estimators for the error distribution in non-parametric regression models can be improved when additional information about the distribution is included by the empirical likelihood method. The weak convergence of the resulting new estimator to a Gaussian process is shown and the performance is investigated by comparison of asymptotic mean squared errors and by means of a simulation study.      

THE ASYMPTOTIC DISTRIBUTIONS OF EMPIRICAL LIKELIHOOD RATIO STATISTICS IN THE PRESENCE OF MEASUREMENT ERROR

Suppose that several different imperfect instruments and one perfect instrument are independently used to measure some characteristics of a population. Thus, measurements of two or more sets of samples with varying accuracies are obtained. Statistical inference should be based on the pooled samples. In this article, the authors also assumes that all the imperfect instruments are unbiased. They consider the problem of combining this information to make statistical tests for parameters more relevant. They define the empirical likelihood ratio functions and obtain their asymptotic distributions in the presence of measurement error.     

Wavelet modeling of priors on triangles

Parameters in statistical problems often live in a geometry of certain shape. For example, count probabilities in a multinomial distribution belong to a simplex. For these problems, Bayesian analysis needs to model priors satisfying certain constraints imposed by the geometry. This paper investigates modeling of priors on triangles by use of wavelets constructed specifically for triangles. Theoretical analysis and numerical simulations show that our modeling is flexible and is superior to the commonly used Dirichlet prior.     

Inference for 2-D GARCH models

The purpose of this paper is, in the first step, to consider a class of GMM estimators with interesting asymptotic properties and a reasonable number of computations for two dimensionally indexed Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model. In the second step, we use the central limit theorem of Huang (1992) for spatial martingale differences to establish the LAN property for general two-dimensional discrete models on a regular grid with Gaussian errors. We then apply this result to the spatial GARCH model and derive the limit distribution of the maximum likelihood estimators of the parameters. Results of numerical simulations are presented.     

Consistent estimation of coefficients in measurement error models with replicated observations

For the estimation of coefficients in a measurement error model, the least squares method utilizing original observations and averaged observations over replications provides inconsistent estimators. Based on these, consistent estimators are formulated and asymptotic properties are analyzed.     

Modified likelihood ratio test for homogeneity in normal mixtures with two samples

This paper investigates the modified likelihood ratio test（LRT） for homogeneity in normal mixtures of two samples with mixing proportions unknown. It is proved that the limit distribution of the modified likelihood ratio test is X^2（1）.     

正态分布的共轭分布及贝叶斯估计

本文介绍含有一个或两个未知参数的正态分布Ｎ（μ，）的共轭分布，以及对正态总体的未知参数进行估计的贝叶斯方法。     

Analysis of multivariate skew normal models with incomplete data

We establish computationally flexible methods and algorithms for the analysis of multivariate skew normal models when missing values occur in the data. To facilitate the computation and simplify the theoretic derivation, two auxiliary permutation matrices are incorporated into the model for the determination of observed and missing components of each observation. Under missing at random mechanisms, we formulate an analytically simple ECM algorithm for calculating parameter estimation and retrieving each missing value with a single-valued imputation. Gibbs sampling is used to perform a Bayesian inference on model parameters and to create multiple imputations for missing values. The proposed methodologies are illustrated through a real data set and comparisons are made with those obtained from fitting the normal counterparts.     

Functional relationships having many independent variables and errors with multivariate normal distribution

This paper deals with maximum likelihood estimation of linear or nonlinear functional relationships assuming that replicated observations have been made on p variables at n points. The joint distribution of the pn errors is assumed to be multivariate normal. Existing results are extended in two ways: first, from known to unknown error covariance matrix; second, from the two variate to the multivariate case.For the linear relationship it is shown that the maximum likelihood point estimates are those obtained by the method of generalized least squares. The present method, however, has the advantage of supplying estimates of the asymptotic covariances of the structural parameter estimates.     

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.     

β-Expectation tolerance regions for a generalized multivariate model with normal error variables

In this paper a procedure of construction of β-expectation tolerance regions in the framework of the structural method of inference has been developed. The procedure has been applied to the generalized multivariate model and the β-expectation tolerance region for this case has been constructed assuming the normal distribution for the error variables of the model.