Maximum likelihood estimation via the ECM algorithm: A general framework

@article{Meng1993MaximumLE,
  title={Maximum likelihood estimation via the ECM algorithm: A general framework},
  author={Xiao-Li Meng and Donald B. Rubin},
  journal={Biometrika},
  year={1993},
  volume={80},
  pages={267-278}
}
Two major reasons for the popularity of the EM algorithm are that its maximum step involves only complete-data maximum likelihood estimation, which is often computationally simple, and that its convergence is stable, with each iteration increasing the likelihood. When the associated complete-data maximum likelihood estimation itself is complicated, EM is less attractive because the M-step is computationally unattractive. In many cases, however, complete-data maximum likelihood estimation is… 
Expectation Maximization Algorithm
The expectation maximization (EM) algorithm is a powerful tool for finding maximum-likelihood estimates in problems where the data are incomplete. Missing data may be an intrinsic feature of the
The restricted EM algorithm under inequality restrictions on the parameters
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
The Statistical Art of Maximizing the Likelihood
The maximum likelihood method is the most popular method in the statistical community for obtaining reasonable estimators for the unknown parameters of a family of distributions. In simple cases the
ML Estimation of the Multivariate t Distribution and the EM Algorithm
TLDR
The results show that the new versions of the ECME algorithm for maximum likelihood estimation of the multivariate t distribution from data with possibly missing values converge faster than the previous procedures.
Maximum Conditional Likelihood via Bound Maximization and the CEM Algorithm
TLDR
The CEM algorithm is presented as an extension of the EM (Expectation Maximization) algorithm to conditional density estimation under missing data and a bounding and maximization process is given to specifically optimize conditional likelihood instead of the usual joint likelihood.
Computational aspects of fitting mixture models via the expectation-maximization algorithm
Multi-user Detection Based on the ECM Iterative Algorithm in Gaussian Noise
TLDR
A novel approach for multi-user detection based on the ECM iterative algorithm that reduces the computational complexity of the M-step and has well performance and Convergence in Gaussian noise.
Maximum likelihood for the multinomial probit model
TLDR
A framework to perform maximum likelihood estimation of the multinomial probit model using a Monte Carlo EM algorithm that includes a Gibbs step and takes advantage of the underlying continuum to simplify calculations.
The EM algorithm for ML Estimators under nonlinear inequalities restrictions on the parameters
TLDR
This paper proposes an asymptotic maximum likelihood estimation procedure under a set of nonlinear inequalities restrictions on the parameters, in which the EM algorithm can be used.
...
...

References

SHOWING 1-10 OF 22 REFERENCES
ON THE CONVERGENCE PROPERTIES OF THE EM ALGORITHM
Two convergence aspects of the EM algorithm are studied: (i) does the EM algorithm find a local maximum or a stationary value of the (incompletedata) likelihood function? (ii) does the sequence of
Globally convergent algorithms for maximizing a likelihood function
SUMMARY In this paper we show global convergence, under very general assumptions, of iterative maximization procedures with cyclic fixing of groups of parameters, maximizing over the remaining
Inference from Iterative Simulation Using Multiple Sequences
TLDR
The focus is on applied inference for Bayesian posterior distributions in real problems, which often tend toward normal- ity after transformations and marginalization, and the results are derived as normal-theory approximations to exact Bayesian inference, conditional on the observed simulations.
Using EM to Obtain Asymptotic Variance-Covariance Matrices: The SEM Algorithm
TLDR
This article defines and illustrates a procedure that obtains numerically stable asymptotic variance–covariance matrices using only the code for computing the complete-data variance-covarance matrix, the code of the expectation maximization algorithm, and code for standard matrix operations.
Unbalanced repeated-measures models with structured covariance matrices.
TLDR
This work addresses the question of how to analyze unbalanced or incomplete repeated-measures data through maximum likelihood analysis using a general linear model for expected responses and arbitrary structural models for the within-subject covariances.
Monte Carlo Sampling Methods Using Markov Chains and Their Applications
SUMMARY A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and
INFERENCE AND MISSING DATA
Two results are presented concerning inference when data may be missing. First, ignoring the process that causes missing data when making sampling distribution inferences about the parameter of the
An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias
Abstract In this paper a method of estimating the parameters of a set of regression equations is reported which involves application of Aitken's generalized least-squares [1] to the whole system of
Statistical Analysis with Missing Data.
Preface.PART I: OVERVIEW AND BASIC APPROACHES.Introduction.Missing Data in Experiments.Complete-Case and Available-Case Analysis, Including Weighting Methods.Single Imputation Methods.Estimation of
On the Statistical Analysis of Dirty Pictures
may 7th, 1986, Professor A. F. M. Smith in the Chair] SUMMARY A continuous two-dimensional region is partitioned into a fine rectangular array of sites or "pixels", each pixel having a particular
...
...