Date: 2019-01-18

Time: 15:30-16:30

Location: BURN 1205

Abstract:

Non-singularity of the information matrix plays a key role in model identification and the asymptotic theory of statistics. For many statistical models, however, this condition seems virtually impossible to verify. An example of such models is a class of mixture models associated with multi-path change-point problems (MCP) which can model longitudinal data with change points. The MCP models are similar in nature to mixture-of-experts models in machine learning. The question then arises as to how often the non-singularity assumption of the information matrix fails to hold. We show that

the set of singularities of the information matrix is a nowhere dense set, i.e. geometrically negligible, if the model is identifiable and some mild smoothness conditions hold. Under further smoothness conditions we show that the set is also of measure zero, i.e. both geometrically and analytically negligible. In view of these results, we further study class of semiparametric MCP models, thus paving the way for establishing asymptotic normality of the maximum likelihood estimates (MLE) and statistical inference of the unknown parameters in such models.

Speaker

Masoud Asgharian is a Professor in the Department of Mathematics and Statistics at McGill University. His research interest is on survival analysis, change-point problems, causal inference, and variable selection.