In this paper we suggest the use of simulation techniques to extend the applicability of the usual Gaussian state space filtering and smoothing techniques to a class of non-Gaussian time series models. This allows a f...
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In this paper we suggest the use of simulation techniques to extend the applicability of the usual Gaussian state space filtering and smoothing techniques to a class of non-Gaussian time series models. This allows a fully Bayesian or maximum likelihood analysis of some interesting models, including outlier models, discrete Markov chain components, multiplicative models and stochastic variance models. Finally we discuss at some length the use of a non-Gaussian model to seasonally adjust the published money supply figures.
This paper is concerned with the inference of incomplete data when the missing data process is non-ignorable in the sense of Rubin (Biometrica 38 (1982) 963-974). With the random effects model and the proposed missing...
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This paper is concerned with the inference of incomplete data when the missing data process is non-ignorable in the sense of Rubin (Biometrica 38 (1982) 963-974). With the random effects model and the proposed missing data process, the conditions missing at random (MAR) and distinct parameters (DP) are discussed. The impact of the missing data is illustrated by the asymptotic bias of the sample mean based on only the observed data and ignoring the missing data process. Maximum likelihood and moment estimators of the marginal mean are obtained.
Statistical problems in modelling personal-income distributions include estimation procedures, testing, and model choice. Typically, the parameters of a given model are estimated by classical procedures such as maximu...
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Statistical problems in modelling personal-income distributions include estimation procedures, testing, and model choice. Typically, the parameters of a given model are estimated by classical procedures such as maximum-likelihood and least-squares estimators. Unfortunately, the classical methods are very sensitive to model deviations such as gross errors in the data, grouping effects, or model misspecifications. These deviations can ruin the values of the estimators and inequality measures and can produce false information about the distribution of the personal income in a country. In this paper we discuss the use of robust techniques for the estimation of income distributions. These methods behave like the classical procedures at the model but are less influenced by model deviations and can be applied to general estimation problems.
In this paper we discuss the potentials of a new Bayesian inference tool, called the ''Gibbs sampler'', for the analysis of the censored regression or Tobit model. Tobit models have a wide range of app...
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In this paper we discuss the potentials of a new Bayesian inference tool, called the ''Gibbs sampler'', for the analysis of the censored regression or Tobit model. Tobit models have a wide range of applications in empirical sciences, like econometrics and biometrics. The estimation results of the simple Tobit model will be compared to a hierarchical Tobit model, and the Gibbs sampling approach to the related classical algorithm of expectation-maximisation (em). The underlying botanical example of this paper is concerned with the censoring mechanism in plant reproduction and proposes the Bayesian Tobit model for the growth relationship between the reproductive part and the rest of the plant.
Equally weighted mixture models are recommended for situations where it is required to draw precise finite sample inferences requiring population parameters, but where the population distribution is not constrained to...
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Equally weighted mixture models are recommended for situations where it is required to draw precise finite sample inferences requiring population parameters, but where the population distribution is not constrained to belong to a simple parametric family. They lead to an alternative procedure to the Laird-DerSimonian maximum likelihood algorithm for unequally weighted mixture models. Their primary purpose lies in the facilitation of exact Bayesian computations via importance sampling. Under very general sampling and prior specifications, exact Bayesian computations can be based upon an application of importance sampling, referred to as Permutable Bayesian Marginalization (PBM). An importance function based upon a truncated multivariate t-distribution is proposed, which refers to a generalization of the maximum likelihood procedure. The estimation of discrete distributions, by binomial mixtures, and inference for survivor distributions, via mixtures of exponential or Weibull distributions, are considered. Equally weighted mixture models are also shown to lead to an alternative Gibbs sampling methodology to the Lavine-West approach.
This paper considers the estimation of mixing proportions when, in addition to the mixture sample, there are available autoregressively dependent data of known origin from each of the classes which make up the mixture...
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This paper considers the estimation of mixing proportions when, in addition to the mixture sample, there are available autoregressively dependent data of known origin from each of the classes which make up the mixture population. An asymptotic variance of the usual discriminant analysis (or confusion matrix) estimator of the mixing proportion is obtained under this condition of correlated training data. The maximum likelihood estimator of the mixing proportion and the associated asymptotic variance are also obtained. A simulation experiment is used to investigate the behaviour of these estimators.
Bootstrap is a time-honoured distribution-free approach for attaching standard error to any statistic of interest, but has not received much attention for data with missing values especially when using imputation tech...
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Bootstrap is a time-honoured distribution-free approach for attaching standard error to any statistic of interest, but has not received much attention for data with missing values especially when using imputation techniques to replace missing values. We propose a proportional bootstrap method that allows effective use of imputation techniques for all bootstrap samples. Five deterministic imputation techniques are examined and particular emphasis is placed on the estimation of standard error for correlation coefficient. Some real data examples are presented. Other possible applications of the proposed bootstrap method are discussed.
We consider the problem min SIGMA(i=1)m ([a(i), x] - b(i) log [a(i), z]) subject to x greater-than-or-equal-to 0 which occurs as a maximum-likelihood estimation problem in several areas, and particularly in positron e...
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We consider the problem min SIGMA(i=1)m ([a(i), x] - b(i) log [a(i), z]) subject to x greater-than-or-equal-to 0 which occurs as a maximum-likelihood estimation problem in several areas, and particularly in positron emission tomography. After noticing that this problem is equivalent to min d(b, Ax) subject to x greater-than-or-equal-to 0, where d is the Kullback-Leibler information divergence and A, b are the matrix and vector with rows and entries a(i), b(i), respectively, we suggest a regularized problem min d(b, Ax) + mud(v, Sx), where mu is the regularization parameter, S is a smoothing matrix, and v is a fixed vector. We present a computationally attractive algorithm for the regularized problem, establish its convergence, and show that the regularized solutions, as mu goes to 0, converge to the solution of the original problem which minimizes a convex function related to d(v, Sx). We give convergence-rate results both for the regularized solutions and for their functional values.
作者：
GRIM, JACAD SCI CZECH REPUBL
INST INFORMAT THEORY & AUTOMATPOD VODARENSKOU VEZI 4CR-18208 PRAGUE 8CZECH REPUBLIC
The input and output information of the probabilistic expert system PES is expressed in terms of discrete random variables, the uncertainty of variables is characterized by discrete probability distributions. The know...
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The input and output information of the probabilistic expert system PES is expressed in terms of discrete random variables, the uncertainty of variables is characterized by discrete probability distributions. The knowledge base of PES has the form of a finite distribution mixture of product components which enables a simple computation of marginal and conditional distributions. The inference mechanism is fully defined by the formula of complete probability and reduces to conditional probability distribution in case of definite input information;The expert system PES was implemented on PC and applied to several problems.
This paper examines the formation of maximum likelihood estimates of cell means in analysis of variance problems for cells with missing observations. Methods of estimating the means for missing cells has a long histor...
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This paper examines the formation of maximum likelihood estimates of cell means in analysis of variance problems for cells with missing observations. Methods of estimating the means for missing cells has a long history which includes iterative maximum likelihood techniques, approximation techniques and ad hoc techniques. The use of the em algorithm to form maximum likelihood estimates has resolved most of the issues associated with this problem. Implementation of the em algorithm entails specification of a reduced model. As demonstrated in this paper, when there are several missing cells, it is possible to specify a reduced model that results in an unidentifiable likelihood. The em algorithm in this case does not converge, although the slow divergence may often be mistaken by the unwary as convergence. This paper presents a simple matrix method of determining whether or not the reduced model results in an identifiable likelihood, and consequently in an em algorithm that converges. We also show the em algorithm in this case to be equivalent to a method which yields a closed form solution.
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