## Kristján Jónasson, University of Iceland.

Math colloquium

**Speakers: **Kristján Jónasson, University of Iceland.

**Title: **Maximum likelihood estimation of multivariate normal parameters when values are missing.

Room: Via Zoom. Link to be sent.

Time: Friday 18^{th} September, 10:00am

#### Abstract:

I have been working on a program to estimate the covariance matrix of a multivariate normal distribution in the presence of missing values via maximum likelihood. Many programs offer to do this by computing pairwise covariances (giving a potentially non-positive-definite matrix). There is a package in R (*mvnmle*) to do the ML-computation, but it is inefficient on several counts. Matlab’s statistical toolbox has a function *mvnmle*, and its financial toolbox has *ecmnmle* which are both quite fast, but they lack flexibility, for example to incorporate REML to eliminate bias, to use regularization (when many values are missing), or to reduce the number of parameters by incorporating some variance structure.

This work is in progress and still unpublished but preliminary results are promising. In the talk I shall tell you a little about the program and the underlying algorithms.