Professor B. L. S. Prakasa Rao, Jawaharlal Nehru Chair Professor Department of Mathematics and Statistics, University of Hyderabad, will be delivering the second Distinguished Lecture Series in the Department of Mathematics next week. The series is entitled " Lectures on Inference for Stochastic Processes". There will three one and half-hour lectures on the 21st, 23rd and 25th of May, 2007 at 4:00 p.m.
Speaker: B. L. S. Prakasa Rao (University of Hyderabad)
Title : Lectures on Inference for Stochastic Processes
Time(s): 4:00 p.m., May 21, 23, and 25, 2007
Venue : Ramanujan Hall, Department of Mathematics, IIT Bombay
Abstract: We study properties of maximum likelihood estimator for nonregular statistical problems through the limiting properties of log-likelihood ratio process in the classical i.i.d framework. After a brief introduction of martingales and limit theorems for martingales, we introduce the concept of conditional Fisher information and study the properties of maximum likelihood estimators for discrete time stochastic processes such as branching processes. Use of Neyman-Pearson lemma in the context of testing a simple hypothesis versus simple alternative for probability measures defined on function spaces will be investigated. The Radon-Nikodym derivative replaces the concept of likelihhod function for continuous time stocahstic processes. After a basic introduction of stochastic differential equations, we investigate the properties of maximum likelihood estimator for the drift coefficient for diffusion processes.