Showing papers on "Expectation–maximization algorithm published in 1969"

A general approach to confirmatory maximum likelihood factor analysis

Abstract: We describe a general procedure by which any number of parameters of the factor analytic model can be held fixed at any values and the remaining free parameters estimated by the maximum likelihood method. The generality of the approach makes it possible to deal with all kinds of solutions: orthogonal, oblique and various mixtures of these. By choosing the fixed parameters appropriately, factors can be defined to have desired properties and make subsequent rotation unnecessary. The goodness of fit of the maximum likelihood solution under the hypothesis represented by the fixed parameters is tested by a large samplex 2 test based on the likelihood ratio technique. A by-product of the procedure is an estimate of the variance-covariance matrix of the estimated parameters. From this, approximate confidence intervals for the parameters can be obtained. Several examples illustrating the usefulness of the procedure are given.

Maximum Likelihood Estimation of the Parameters of the Gamma Distribution and Their Bias

Abstract: The numerical technique of the maximum likelihood method to estimate the parameters of Gamma distribution is examined. A convenient table is obtained to facilitate the maximum likelihood estimation of the parameters and the estimates of the variance-covariance matrix. The bias of the estimates is investigated numerically. The empirical result indicates that the bias of both parameter estimates produced by the maximum likelihood method is positive.

A Newton-Raphson algorithm for maximum likelihood factor analysis

Abstract: This paper demonstrates the feasibility of using a Newton-Raphson algorithm to solve the likelihood equations which arise in maximum likelihood factor analysis. The algorithm leads to clean easily identifiable convergence and provides a means of verifying that the solution obtained is at least a local maximum of the likelihood function. It is shown that a popular iteration algorithm is numerically unstable under conditions which are encountered in practice and that, as a result, inaccurate solutions have been presented in the literature. The key result is a computationally feasible formula for the second differential of a partially maximized form of the likelihood function. In addition to implementing the Newton-Raphson algorithm, this formula provides a means for estimating the asymptotic variances and covariances of the maximum likelihood estimators.

Method of Maximum Likelihood Applied to the Analysis of Flashover Data

Abstract: Maximum likelihood methods are applied to the analysis of flashover probability data. A two-parameter distribution is assumed, with emphasis on the normal distribution. Variances and approximate confidence limits are determined.

Recursive maximum likelihood estimates using the Ito calculus

Abstract: Showing that a certain maximum likelihood estimate of the initial state of a nonlinear system is an Ito process asymptotically is considered. Also using the Ito calculus, a scalar recursive estimator equation is derived.