In this article, a new method is proposed for clustering longitudinal curves. In the proposed method, clusters of mean functions are identified through a weighted concave pairwise fusion method. The em algorithm and t...
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In this article, a new method is proposed for clustering longitudinal curves. In the proposed method, clusters of mean functions are identified through a weighted concave pairwise fusion method. The em algorithm and the alternating direction method of multipliers algorithm are combined to estimate the group structure, mean functions and principal components simultaneously. The proposed method also allows to incorporate the prior neighborhood information to have more meaningful groups by adding pairwise weights in the pairwise penalties. In the simulation study, the performance of the proposed method is compared to some existing clustering methods in terms of the accuracy for estimating the number of subgroups and mean functions. The results suggest that ignoring the covariance structure will have a great effect on the performance of estimating the number of groups and estimating accuracy. The effect of including pairwise weights is also explored in a spatial lattice setting to take into consideration of the spatial information. The results show that incorporating spatial weights will improve the performance. A real example is used to illustrate the proposed method.
Latent class analysis is formulated as a problem of estimating parameters in a finite mixture distribution. The em algorithm is used to find the maximum likelihood estimates, and the case of categorical variables with...
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Latent class analysis is formulated as a problem of estimating parameters in a finite mixture distribution. The em algorithm is used to find the maximum likelihood estimates, and the case of categorical variables with more than two categories is considered.
Accurately estimating the timing of pathogen exposure plays a crucial role in outbreak control for emerging infectious diseases, including the source identification, contact tracing, and vaccine research and developme...
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Accurately estimating the timing of pathogen exposure plays a crucial role in outbreak control for emerging infectious diseases, including the source identification, contact tracing, and vaccine research and development. However, since surveillance activities often collect data retrospectively after symptoms have appeared, obtaining accurate data on the timing of disease onset is difficult in practice and can involve "coarse" observations, such as interval or censored data. To address this challenge, we propose a novel likelihood function, tailored to coarsely observed data in rapid outbreak surveillance, along with an optimization method based on an e-accelerated em algorithm for faster convergence to find maximum likelihood estimates (MLEs). The covariance matrix of MLEs is also discussed using a nonparametric bootstrap approach. In terms of bias and mean-squared error, the performance of our proposed method is evaluated through extensive numerical experiments, as well as its application to a series of epidemiological surveillance focused on cases of mass food poisoning. The experiments show that our method exhibits less bias than conventional methods, providing greater efficiency across all scenarios.
The stochastic em algorithm is a widely applicable approach for computing maximum likelihood estimates for the mixture problem. We present here an extension of the Sem algorithm in a particular case of incomplete data...
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The stochastic em algorithm is a widely applicable approach for computing maximum likelihood estimates for the mixture problem. We present here an extension of the Sem algorithm in a particular case of incomplete data, where the loss of information is due both to mixture models and censored observations. We propose several solutions to implement the 'Semcm algorithm' (Sem for censored mixture), showing in particular that one of these procedures solves numerical problems arising with the emcm algorithm and mixtures of nonexponential-type distributions. Theoretically, we study the asymptotic behavior of Semcm in the simple case of a two-component censored mixture, where the unknown parameter is the mixing proportion. We prove, for each Semcm procedures, convergence of the stationary distribution to a Gaussian distribution located on the m.l.e. of the parameter. To conclude, we give some examples based on simulations for censored samples with a great amount of lost information.
The em algorithm is a much used tool for maximum likelihood estimation in missing or incomplete data problems. However, calculating the conditional expectation required in the E-step of the algorithm may be infeasible...
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The em algorithm is a much used tool for maximum likelihood estimation in missing or incomplete data problems. However, calculating the conditional expectation required in the E-step of the algorithm may be infeasible, especially when this expectation is a large sum or a high-dimensional integral. Instead the expectation can be estimated by simulation. This is the common idea in the stochastic em algorithm and the Monte Carlo em algorithm. In this paper some asymptotic results for the Stochastic em algorithm are given, and estimation based on this algorithm is discussed. In particular, asymptotic equivalence of certain simple estimators is shown, and a simulation experiment is carried out to investigate this equivalence in small and moderate samples. Furthermore, some implementation issues and the possibility of allowing unidentified parameters in the algorithm are discussed.
This note addresses a problem that can arise in surveys, namely when some respondents misinterpret the rating method and so assign high ratings when they intended to assign low ratings, and vice versa. We present a me...
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This note addresses a problem that can arise in surveys, namely when some respondents misinterpret the rating method and so assign high ratings when they intended to assign low ratings, and vice versa. We present a method that allows these misinterpretations to be corrected with high probability, and more meaningful conclusions to be drawn. The method is illustrated with data from a Community Value survey.
In screening and surveillance studies, event times are interval censored. Besides, screening tests are imperfect so that the interval at which an event takes place may be uncertain. We describe an expectation-maximiza...
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In screening and surveillance studies, event times are interval censored. Besides, screening tests are imperfect so that the interval at which an event takes place may be uncertain. We describe an expectation-maximization algorithm to find the nonparametric maximum likelihood estimator of the cumulative incidence function of an event based on screening test data. Our algorithm has a closed-form solution for the combined expectation and maxi-mization step and is computationally undemanding. A simulation study indicated that the bias of the estimator tends to zero for large sample size, and its mean squared error is in general lower than the mean squared error of the estimator that assumes the screening test is perfect. We apply the algorithm to follow-up data from women treated for cervical precancer. Copyright (C) 2017 John Wiley & Sons, Ltd.
Two algorithms are compared for maximizing the likelihood function associated with parameter estimation in partially observed diffusion processes: • • the em algorithm, investigated by Dembo and Zeitouni (...
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Two algorithms are compared for maximizing the likelihood function associated with parameter estimation in partially observed diffusion processes: • • the em algorithm, investigated by Dembo and Zeitouni (1986), an iterative algorithm where, at each iteration, an auxiliary function is computed and maximized; • • the direct approach where the likelihood function itself is computed and maximized. This yields to a comparison of nonlinear smoothing and nonlinear filtering for computing a class of conditional expectations related to the problem of estimation. In particular, it is shown that smoothing is indeed necessary for the em algorithm approach to be efficient. Time discretization schemes for the stochastic PDE's involved in the algorithms are given, and the link with the discrete time case (hidden Markov model) is explored. Numerical results are presented with the conclusion that direct maximization should be preferred whenever some noise covariances associated with the parameters to be estimated are small.
One of the most powerful algorithms for maximum likelihood estimation for many incomplete-data problems is the em algorithm. The restricted em algorithm for maximum likelihood estimation under linear restrictions on t...
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One of the most powerful algorithms for maximum likelihood estimation for many incomplete-data problems is the em algorithm. The restricted em algorithm for maximum likelihood estimation under linear restrictions on the parameters has been handled by Kim and Taylor (J. Amer. Statist. Assoc. 430 (1995) 708-716). This paper proposes an em algorithm for maximum likelihood estimation under inequality restrictions A(0beta)greater than or equal to0, where beta is the parameter vector in a linear model W = Xbeta + epsilon and epsilon is an error variable distributed normally with mean zero and a known or unknown variance matrix Sigma > 0. Some convergence properties of the ENT sequence are discussed. Furthermore, we consider the consistency of the restricted em estimator and a related testing problem. (C) 2003 Elsevier Inc. All rights reserved.
Based on progressively type-II censored data, the maximum-likelihood estimators (MLEs) for the Lomax parameters are derived using the expectation-maximization (em) algorithm. Moreover, the expected Fisher information ...
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Based on progressively type-II censored data, the maximum-likelihood estimators (MLEs) for the Lomax parameters are derived using the expectation-maximization (em) algorithm. Moreover, the expected Fisher information matrix based on the missing value principle is computed. Using extensive simulation and three criteria, namely, bias, root mean squared error and Pitman closeness measures, we compare the performance of the MLEs via the em algorithm and the Newton-Raphson (NR) method. It is concluded that the em algorithm outperforms the NR method in all the cases. Two real data examples are used to illustrate our proposed estimators.
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