Sponsoring Section/Society: ASA, IMS, IISA
Session Slot: 2:00- 3:50 Monday
Estimated Audience Size: xx-xxx
AudioVisual Request: None
Session Title: R. R. Bahadur Memorial Session
Theme Session: No
Applied Session: No
Session Organizer: Stigler, Stephen M. University of Chicago
Address: Department of Statistics 5734 University Ave. Chicago, IL 60637
Phone: 773-702-8328
Fax: 773-955-5893
Email: stigler@galton.uchicago.edu
Session Timing: 110 minutes total (Sorry about format):
Opening Remarks by Chair - 5 minutes First Speaker - 30 minutes Second Speaker - 30 minutes Third Speaker - 30 minutes Floor Discusion - 10 minutes
Session Chair: Stigler, Stephen M. University of Chicago
Address: Department of Statistics 5734 University Ave. Chicago, IL 60637
Phone: 773-702-8328
Fax: 773-955-5893
Email: stigler@galton.uchicago.edu
1. Bahadur and Sufficiency
Diaconis, Persi, Cornell University
Address: Mathematics Department White Hall Cornell University Ithaca, NY 14853
Phone:
Fax:
Email: ims@math.cornell.edu
Abstract: Bahadur's work on sufficiency illuminated sequential analysis, Bayesian decision theory, and mathematical statistics generally.
2. Consistency Issues For Maximum Likelihood Estimates and Bayesian Analysis
Ghosh, Jayanta K., ISI and Purdue University
Address: Department of Statistics Purdue University West Lafayette, IN 47907, and Theoretical Statistics and Mathematics, ISI, 203 B.T. Road, Calcutta 700 035, INDIA
Phone:
Fax:
Email: ghosh@stat.purdue.edu
Ramamoorthi, R.V., ISI
Ghosal, S., ISI
Abstract: Bahadur was the first to raise in 1958 the question of consistency of the maximum likelihood estimate of the true density and later provided a definitive answer through a theorem and counterexamples. His treatment was nonparametric in spirit. Some work has been done recently on the convergence of non parametric maximum likelihood estimates, based on empirical processes. There are related questions of consistency of the posterior in non parametric infinite dimensional Bayesian analysis, as in Diaconis and Freedman (Annals of Statistics, 1986). In this area too, for example in Bayesian density estimation, there have been significant new developments. My review will begin with a look at Bahadur's work and then provide a relatively non-technical and self contained survey of recent work.
3. Bahadur and Asymptotic Efficiency Theory
Address: UCLA Interdivisional Program in Statistics 8118 Mathematical Sciences, 155404 Box 951554 Los Angeles, CA 90095-1554
Phone:
Fax: (310) 206-5658
Email: whwong@stat.ucla.edu
Shen, Xiaotong, Ohio State University
Abstract: Raj Bahadur had made fundamental contributions to the study of asymptotic efficiency in estimation and testing. We review two aspects of his impact in this area. First, his paper in 1964 clarified the best possible performance for estimators that possess asymptotic distributions. This work represented an elegant completion of a series of deep studies on this issue by Edgeworth, Fisher and LeCam. A second and perhaps more profound contribution by Bahadur was an alternative approach to asymptotics based on large deviation probability. His 1960 paper introduced global and local bounds for the best possible rate, known as Bahadur efficiency, by an application of the Neyman-Pearson Lemma. This work had stimulated much subsequent research by many other investigators. It was a great leap that added immensely to our understanding of many fundamental issues in estimation and testing.
List of speakers who are nonmembers: None