Standard errors for EM estimation

    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

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