Title

Standard errors for EM estimation

Authors

Authors

M. Jamshidian;R. I. Jennrich

Abbreviated Journal Title

J. R. Stat. Soc. Ser. B-Stat. Methodol.

Keywords

asymptotic variance-covariance matrix; EM algorithm; numerical; differentiation; observed information; precision; SEM algorithm; slow; convergence; MAXIMUM-LIKELIHOOD; SURVEILLANCE DATA; ALGORITHM; ACCELERATION; DISTRIBUTIONS; VARIANCE; Statistics & Probability

Abstract

The EM algorithm is a popular method for computing maximum likelihood estimates. One of its drawbacks is that it does not produce standard errors as a by-product. We consider obtaining standard errors by numerical differentiation. Two approaches are considered. The first differentiates the Fisher score vector to yield the Hessian of the log-likelihood. The second differentiates the EM operator and uses an identity that relates its derivative to the Hessian of the log-likelihood. The well-known SEM algorithm uses the second approach. We consider three additional algorithms: one that uses the first approach and two that use the second. We evaluate the complexity and precision of these three and the SEM algorithm in seven examples. The first is a single-parameter example used to give insight. The others are three examples in each of two areas of EM application: Poisson mixture models and the estimation of covariance from incomplete data. The examples show that there are algorithms that are much simpler and more accurate than the SEM algorithm. Hopefully their simplicity will increase the availability of standard error estimates in EM applications. It is shown that, as previously conjectured, a symmetry diagnostic can accurately estimate errors arising from numerical differentiation. Some issues related to the speed of the EM algorithm and algorithms that differentiate the EM operator are identified.

Journal Title

Journal of the Royal Statistical Society Series B-Statistical Methodology

Volume

62

Publication Date

1-1-2000

Document Type

Article

Language

English

First Page

257

Last Page

270

WOS Identifier

WOS:000086433600003

ISSN

1369-7412

Share

COinS