English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Maximum likelihood estimation is a popular method in statistical inference.As a way of assessing the accuracy of the maximum likelihood estimate (MLE),the calculation of the covariance matrix of the MLE is of great interest inpractice. Standard statistical theory shows that the normalized MLE isasymptotically normally distributed with covariance matrix being the inverse ofthe Fisher information matrix (FIM) at the unknown parameter. Two commonly usedestimates for the covariance of the MLE are the inverse of the observed FIM(the same as the inverse Hessian of the negative log-likelihood) and theinverse of the expected FIM (the same as the inverse FIM). Both of the observedand expected FIM are evaluated at the MLE from the sample data. In thisdissertation, we demonstrate that, under reasonable conditions similar tostandard MLE conditions, the inverse expected FIM outperforms the inverseobserved FIM under a mean squared error criterion. Specifically, in anasymptotic sense, the inverse expected FIM (evaluated at the MLE) has nogreater mean squared error with respect to the true covariance matrix than theinverse observed FIM (evaluated at the MLE) at the element level. This resultis different from widely accepted results showing preference for the observedFIM. In this dissertation, we present theoretical derivations that lead to theconclusion above. We also present numerical studies on three distinct problemsto support the theoretical result. This dissertation also includes twoappendices on topics of relevance to stochastic systems. The first appendixdiscusses optimal perturbation distributions for the simultaneous perturbationstochastic approximation (SPSA) algorithm. The second appendix considers MonteCarlo methods for computing FIMs when closed forms are not attainable.

Relative Performance of Expected and Observed Fisher Information in Covariance Estimation for Maximum Likelihood Estimates