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UID:20250312T171730EDT-9520Ua51oc@132.216.98.100
DTSTAMP:20250312T211730Z
DESCRIPTION:Singularities of the information matrix and longitudinal data w
 ith change points.\n\nNon-singularity of the information matrix plays a ke
 y role in model identication and the asymptotic theory of statistics. For 
 many statis- tical models\, however\, this condition seems virtually impos
 sible to verify. An example of such models is a class of mixture models as
 sociated with multi- path change-point problems (MCP) which can model long
 itudinal 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 fa
 ils to hold. We show that the set of singularities of the information matr
 ix is a nowhere dense set\, i.e. geometrically negligible\, if the model i
 s identiable and some mild smoothness conditions hold. Under further smoot
 hness conditions we show that the set is also of measure zero\, i.e. both 
 geometrically and analytically negligible. In view of these results\, we f
 urther study a class of semiparametric MCP models\, thus paving the way fo
 r establishing asymptotic normality of the maximum likelihood estimates (M
 LE) and statistical inference of the unknown parame- ters in such models. 
 References [1] Asgharian\, M. (2014). ON THE SINGULARITIES OF THE INFORMAT
 ION MATRIX AND MULTIPATH CHANGE-POINT PROBLEMS. Theory of Probability and 
 its Appli- cations \, Vol. 58\, No. 4\, pp 546-561\n
DTSTART:20161111T203000Z
DTEND:20161111T213000Z
LOCATION:Room D4-2019\, CA\, Seminar Statistics Sherbrooke\, 2500 boul. de 
 l'Université
SUMMARY:Masoud Asgharian\, 9IÖÆ×÷³§Ãâ·Ñ
URL:/mathstat/channels/event/masoud-asgharian-mcgill-u
 niversity-263936
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