By incorporating the Expectation-maximization (em) algorithm into composite asymmetric Laplace distribution (CALD), an iterative weighted least square estimator for the linear composite quantile regression (CQR) model...
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By incorporating the Expectation-maximization (em) algorithm into composite asymmetric Laplace distribution (CALD), an iterative weighted least square estimator for the linear composite quantile regression (CQR) models is derived. Two selection methods for the number of composite quantiles via redefined AIC and BIC are developed. Finally, the proposed procedures are illustrated by some simulations. (C) 2016 Elsevier B.V. All rights reserved.
Maximum likelihood estimation of item parameters in the marginal distribution, integrating over the distribution of ability, becomes practical when computing procedures based on an em algorithm are used. By characteri...
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Maximum likelihood estimation of item parameters in the marginal distribution, integrating over the distribution of ability, becomes practical when computing procedures based on an em algorithm are used. By characterizing the ability distribution empirically, arbitrary assumptions about its form are avoided. The em procedure is shown to apply to general item-response models lacking simple sufficient statistics for ability. This includes models with more than one latent dimension.
This paper deals with an empirical Bayes approach for spatial prediction of a Gaussian random field. In fact, we estimate the hyperparameters of the prior distribution by using the maximum likelihood method. In order ...
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This paper deals with an empirical Bayes approach for spatial prediction of a Gaussian random field. In fact, we estimate the hyperparameters of the prior distribution by using the maximum likelihood method. In order to maximize the marginal distribution of the data, the em algorithm is used. Since this algorithm requires the evaluation of analytically intractable and high dimensionally integrals, a Monte Carlo method based on discretizing parameter space, is proposed to estimate the relevant integrals. Then, the approach is illustrated by its application to a spatial data set. Finally, we compare the predictive performance of this approach with the reference prior method.
We address the problem of Bayesian variable selection for high-dimensional linear regression. We consider a generative model that uses a spike-and-slab-like prior distribution obtained by multiplying a deterministic b...
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We address the problem of Bayesian variable selection for high-dimensional linear regression. We consider a generative model that uses a spike-and-slab-like prior distribution obtained by multiplying a deterministic binary vector, which traduces the sparsity of the problem, with a random Gaussian parameter vector. The originality of the work is to consider inference through relaxing the model and using a type-II log-likelihood maximization based on an em algorithm. Model selection is performed afterwards relying on Occam's razor and on a path of models found by the em algorithm. Numerical comparisons between our method, called spinyReg, and state-of-the-art high-dimensional variable selection algorithms (such as lasso, adaptive lasso, stability selection or spike and-slab procedures) are reported. Competitive variable selection results and predictive performances are achieved on both simulated and real benchmark data sets. An original regression data set involving the prediction of the number of visitors of the Orsay museum in Paris using bike-sharing system data is also introduced, illustrating the efficiency of the proposed approach. The R package spinyReg implementing the method proposed in this paper is available on CRAN. (C) 2015 Elsevier Inc. All rights reserved.
A new acceleration scheme for optimization procedures is defined through geometric considerations and applied to the em algorithm. In many cases it is able to circumvent the problem of stagnation. No modification of t...
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A new acceleration scheme for optimization procedures is defined through geometric considerations and applied to the em algorithm. In many cases it is able to circumvent the problem of stagnation. No modification of the original algorithm is required. It is simply used as a software component. Thus the new scheme can be easily implemented to accelerate a fixed point algorithm maximizing some objective function. Some practical examples and simulations are presented to show its ability to accelerate em-type algorithms converging slowly.
In linear mixed models, the assumption of normally distributed random effects is often inappropriate and unnecessarily restrictive. The proposed approximate Dirichlet process mixture assumes a hierarchical Gaussian mi...
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In linear mixed models, the assumption of normally distributed random effects is often inappropriate and unnecessarily restrictive. The proposed approximate Dirichlet process mixture assumes a hierarchical Gaussian mixture that is based on the truncated version of the stick breaking presentation of the Dirichlet process. In addition to the weakening of distributional assumptions, the specification allows to identify clusters of observations with a similar random effects structure. An Expectation-Maximization algorithm is given that solves the estimation problem and that, in certain respects, may exhibit advantages over Markov chain Monte Carlo approaches when modelling with Dirichlet processes. The method is evaluated in a simulation study and applied to the dynamics of unemployment in Germany as well as lung function growth data.
Let Y=(Y-t)(t greater than or equal to 0) be an unobserved random process which influences the distribution of a random variable T which can be interpreted as the time to failure. When a conditional hazard rate corres...
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Let Y=(Y-t)(t greater than or equal to 0) be an unobserved random process which influences the distribution of a random variable T which can be interpreted as the time to failure. When a conditional hazard rate corresponding to T is a quadratic function of covariates, Y, the marginal survival function may be represented by the first two moments of the conditional distribution of Y among survivors. Such a representation may not have an explicit parametric form. This makes it difficult to use standard maximum likelihood procedures to estimate parameters - especially for censored survival data. In this paper a generalization of the em algorithm for survival problems with unobserved, stochastically changing covariates is suggested. It is shown that, for a general model of the stochastic failure model, the smoothing estimates of the first two moments of Y are of a specific form which facilitates the em type calculations. Properties of the algorithm are discussed.
Some patterned covariance matrices used to model multivariate normal data that do not have explicit maximum likelihood estimates can be viewed as submatrices of larger patterned covariance matrices that do have explic...
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Some patterned covariance matrices used to model multivariate normal data that do not have explicit maximum likelihood estimates can be viewed as submatrices of larger patterned covariance matrices that do have explicit maximum likelihood estimates. In such cases, the smaller covariance matrix can be viewed as the covariance matrix for observed variables and the larger covariance matrix can be viewed as the covariance matrix for both observed and missing variables. The advantage of this perspective is that the em algorithm can be used to calculate the desired maximum likelihood estimates for the original problem. Two examples are presented.
The classical em algorithm for the restoration of the mixture of normal probability distributions cannot determine the number of components in the mixture. An algorithm called ARD em for the automatic determination of...
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The classical em algorithm for the restoration of the mixture of normal probability distributions cannot determine the number of components in the mixture. An algorithm called ARD em for the automatic determination of the number of components is proposed, which is based on the relevance vector machine. The idea behind this algorithm is to use a redundant number of mixture components at the first stage and then determine the relevant components by maximizing the evidence. Experiments with model problems show that the number of clusters thus determined either coincides with the actual number or slightly exceeds it. In addition, clusterization using ARD em turns out to be closer to the actual clusterization than that obtained by the analogs based on cross validation and the minimum description length principle.
We consider novel methods for the Computation of model selection criteria in missing-data problems based on the output of the em algorithm The methodology is very general and can be applied to numerous simulations inv...
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We consider novel methods for the Computation of model selection criteria in missing-data problems based on the output of the em algorithm The methodology is very general and can be applied to numerous simulations involving incomplete data within an em framework, from covariates missing at random in arbitrary regression models to nonignorably missing longitudinal responses and/or covariates. Toward this goal, we develop a class of information criteria for missing-data problems called ICH,Q, which yields the Akaike information criterion and the Bayesian information criterion as special cases. The computation of ICH,Q requires an analytic approximation to a complicated function. called the H-function, along with output from the em algorithm used in obtaining maximum likelihood estimates. The approximation to the H-function leads to a large class of information criteria, called IC(H) over tilde (k),Q. Theoretical properties of IC(H) over tilde (k),Q, including consistency, are investigated in detail. To eliminate the analytic approximation to the H-function, a computationally simpler approximation to ICH,Q. called ICQ, is proposed, the computation of which depends solely on the Q-function of the em algorithm. Advantages and disadvantages of IC(H) over tilde (k),Q and ICQ are discussed and examined in detail in the context of missing-data problems. Extensive simulations are given to demonstrate the methodology and examine the small-sample and large-sample performance of IC(H) over tilde (k),Q and ICQ in missing-data problems. An AIDS data set also is presented to illustrate the proposed methodology.
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