In this paper,ve discuss graphical models for mixed types of continuous and discrete variables with incomplete data. We use a set of hyperedges to represent an observed data pattern. A hyperedge is a set of variables ...
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In this paper,ve discuss graphical models for mixed types of continuous and discrete variables with incomplete data. We use a set of hyperedges to represent an observed data pattern. A hyperedge is a set of variables observed for a group of individuals. In a mixed graph with two types of vertices and two types of edges, dots and circles represent discrete and continuous variables respectively. A normal graph represents a graphical model and a hypergraph represents an observed data pattern. In terms of the mixed graph, we discuss decomposition of mixed graphical models with incomplete data, and we present a partial imputation method which ran be used in the em algorithm and the Gibbs sampler to speed their convergence. For a given mixed graphical model and an observed data pattern, we try to decompose a large graph into several small ones so that the original likelihood can be factored into a product of likelihoods with distinct parameters for small graphs. For the case that a graph cannot be decomposed due to its observed data pattern, we can impute missing data partially so that the graph can be decomposed.
In this paper we study the maximum likelihood estimation of parameters, of the bivariate Poisson distribution, by assuming a sample with a general pattern of missing observations and applying the em algorithm (Dempste...
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In this paper we study the maximum likelihood estimation of parameters, of the bivariate Poisson distribution, by assuming a sample with a general pattern of missing observations and applying the em algorithm (Dempster, Laird and Rubin, 1977). The application of the method is outlined in the complete-data estimation problem, considered by Holgate (1964), since the latter can be viewed as a special case of the missing-value problem studied here. The observed information matrix is also obtained by means of the em algorithm (Louis, 1982) and numerical examples are presented. The application of Louis's method is found most appropriate and seen to produce remarkable acceleration in the convergence of the em algorithm. Results of some interest, concerning the conditional distributions of Poisson variables, given particular sums of Poisson random variables are also established.
Analysis of various multi-modal strength distributions are studied by using competing risks models. This multi-modality may arise due to several kinds of flaws in a material. The fracture of a material is controlled b...
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Analysis of various multi-modal strength distributions are studied by using competing risks models. This multi-modality may arise due to several kinds of flaws in a material. The fracture of a material is controlled by the most severe of all the flaws, the so-called 'weakest-link theory', which is also commonly referred to as 'competing risks' in the statistics literature. These multi-modal problems can also be further complicated due to possible censoring. In practice, censoring is very common because of time and cost considerations on experiments. Moreover, in certain situations, it is observed that the mode of failure is not properly identified due to lack of appropriate diagnostics, expensive and time-consuming autopsy, etc. This is known as the masking problem. Several studies have been carried out, but they have mainly focused on bi-modal Weibull distributions with no censoring or masking considered. In this paper, we deal with the strength distribution of multi-modal failures when censoring and masking are present. We provide the em-type parameter estimator for a variety of strength distributions including Weibull, lognormal and inverse Gaussian distributions. The applicability of this method is illustrated by several examples.
We propose a semiparametric version of the em algorithm under the semiparametric mixture model introduced by Anderson (1979, Biometrika , 66 , 17-26). It is shown that the sequence of proposed em iterates, irrespectiv...
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We propose a semiparametric version of the em algorithm under the semiparametric mixture model introduced by Anderson (1979, Biometrika , 66 , 17-26). It is shown that the sequence of proposed em iterates, irrespective of the starting value, converges to the maximum semiparametric likelihood estimator of the vector of parameters in the semiparametric mixture model. The proposed em algorithm preserves the appealing monotone convergence property of the standard em algorithm and can be implemented by employing the standard logistic regression program. We present one example to demonstrate the performance of the proposed em algorithm.
One of the most important problems that arise when estimating parameters by the maximum likelihood method in INAR models, including minification models, is that the estimates cannot be presented in analytical form, bu...
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One of the most important problems that arise when estimating parameters by the maximum likelihood method in INAR models, including minification models, is that the estimates cannot be presented in analytical form, but some numerical method must be used to find them. To solve this problem, we present an em algorithm. As this problem is difficult to solve based on the original definition of the model, in this manuscript, we first show that the model can be presented in an equivalent form. Then, based on that equivalent form, we construct an em algorithm for estimating the parameters of the model. Finally, the quality of the estimates and the speed of the algorithm were observed on the simulated data.
Publication bias occurs when the published research results are systematically unrepresentative of the population of studies that have been conducted, and is a potential threat to meaningful meta-analysis. The Copas s...
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Publication bias occurs when the published research results are systematically unrepresentative of the population of studies that have been conducted, and is a potential threat to meaningful meta-analysis. The Copas selection model provides a flexible framework for correcting estimates and offers considerable insight into the publication bias. However, maximizing the observed likelihood under the Copas selection model is challenging because the observed data contain very little information on the latent variable. In this article, we study a Copas-like selection model and propose an expectation-maximization (em) algorithm for estimation based on the full likelihood. empirical simulation studies show that the em algorithm and its associated inferential procedure performs well and avoids the non-convergence problem when maximizing the observed likelihood.
Regression modelling involving heavy-tailed response distributions, which have heavier tails than the exponential distribution, has become increasingly popular in many insurance settings including non-life insurance. ...
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Regression modelling involving heavy-tailed response distributions, which have heavier tails than the exponential distribution, has become increasingly popular in many insurance settings including non-life insurance. Mixed Exponential models can be considered as a natural choice for the distribution of heavy-tailed claim sizes since their tails are not exponentially bounded. This paper is concerned with introducing a general family of mixed Exponential regression models with varying dispersion which can efficiently capture the tail behaviour of losses. Our main achievement is that we present an Expectation-Maximization (em)-type algorithm which can facilitate maximum likelihood (ML) estimation for our class of mixed Exponential models which allows for regression specifications for both the mean and dispersion parameters. Finally, a real data application based on motor insurance data is given to illustrate the versatility of the proposed em-type algorithm.
We present a maximum likelihood (ML) method for semi-blind estimation of single-input multi-output (SIMO) flat-fading channels in spatially correlated noise having unknown covariance. An expectation-maximization (em) ...
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We present a maximum likelihood (ML) method for semi-blind estimation of single-input multi-output (SIMO) flat-fading channels in spatially correlated noise having unknown covariance. An expectation-maximization (em) algorithm is utilized to compute the ML estimates of the channel and spatial noise covariance. We derive the Cramer-Rao bound (CRB) matrix for the unknown parameters and present a symbol detector that utilizes the em channel estimates. Numerical simulations demonstrate the performance of the proposed method.
The em algorithm is a method for producing a sequence of parameter estimates that, under mild regularity conditions, converges to the MLE. The em algorithm is well regarded, in part because of two monotonicity propert...
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The em algorithm is a method for producing a sequence of parameter estimates that, under mild regularity conditions, converges to the MLE. The em algorithm is well regarded, in part because of two monotonicity properties: convergence to the MLE is monotone, and the value of the Likelihood function increases with each iteration. A graphical illustration of the em algorithm makes these properties intuitively apparent in the one-parameter case. In addition, a well-known result regarding the rate of convergence of the algorithm can be inferred.
One of the estimating equations of the Maximum Likelihood Estimation method, for finite mixtures of the one parameter exponential family, is the first moment equation. This can help considerably in reducing the labor ...
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One of the estimating equations of the Maximum Likelihood Estimation method, for finite mixtures of the one parameter exponential family, is the first moment equation. This can help considerably in reducing the labor and the cost of calculating the Maximum Likelihood estimates. In this paper it is shown that the em algorithm can be substantially improved by using this result when applied for mixture models. A short discussion about other methods proposed for the calculation of the Maximum Likelihood estimates are also reported showing that the above findings can help in this direction too.
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