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Full-Text Articles in Statistics and Probability
Empirical Bayes And Hierarchical Bayes Estimation Of Skew Normal Populations, Naveen K. Bansal, Mehdi Maadooliat, Xiaowei Wang
Empirical Bayes And Hierarchical Bayes Estimation Of Skew Normal Populations, Naveen K. Bansal, Mehdi Maadooliat, Xiaowei Wang
Naveen Bansal
We develop empirical and hierarchical Bayesian methodologies for the skew normal populations through the EM algorithm and the Gibbs sampler. A general concept of skewness to the normal distribution is considered throughout. Motivations are given for considering the skew normal population in applications, and an example is presented to demonstrate why the skew normal distribution is more applicable than the normal distribution for certain applications.
Variances For Maximum Penalized Likelihood Estimates Obtained Via The Em Algorithm, Mark Segal, Peter Bacchetti, Nicholas Jewell
Variances For Maximum Penalized Likelihood Estimates Obtained Via The Em Algorithm, Mark Segal, Peter Bacchetti, Nicholas Jewell
Mark R Segal
We address the problem of providing variances for parameter estimates obtained under a penalized likelihood formulation through use of the EM algorithm. The proposed solution represents a synthesis of two existent techniques. Firstly, we exploit the supplemented EM algorithm developed in Meng and Rubin (1991) that provides variance estimates for maximum likelihood estimates obtained via the EM algorithm. Their procedure relies on evaluating the Jacobian of the mapping induced by the EM algorithm. Secondly, we utilize a result from Green (1990) that provides an expression for the Jacobian of the mapping induced by the EM algorithm applied to a penalized …
Multilevel Latent Class Models With Dirichlet Mixing Distribution, Chong-Zhi Di, Karen Bandeen-Roche
Multilevel Latent Class Models With Dirichlet Mixing Distribution, Chong-Zhi Di, Karen Bandeen-Roche
Chongzhi Di
Latent class analysis (LCA) and latent class regression (LCR) are widely used for modeling multivariate categorical outcomes in social sciences and biomedical studies. Standard analyses assume data of different respondents to be mutually independent, excluding application of the methods to familial and other designs in which participants are clustered. In this paper, we consider multilevel latent class models, in which sub-population mixing probabilities are treated as random effects that vary among clusters according to a common Dirichlet distribution. We apply the Expectation-Maximization (EM) algorithm for model fitting by maximum likelihood (ML). This approach works well, but is computationally intensive when …