IMS
Session Slot: 4:00- 5:50 Tuesday
Estimated Audience Size: xxx
AudioVisual Request: Two Overheads
Session Title: President's Invited Session
Theme Session: No
Applied Session: No
Session Organizer: Diaconis, Persi Cornell University
Address: Department of Mathematics, ORIE, Cornell University
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Fax:
Email: persi@orie.cornell.edu
Session Timing: 110 minutes total (Sorry about format):
usual
Session Chair: Diaconis, Persi Cornell University
Address: Department of Mathematics, ORIE, Cornell University
Phone:
Fax:
Email: persi@orie.cornell.edu
1. Nonparametrics: The Development of a Subdiscipline
Lehmann, Erich, University of California, Berkeley
Address: Statistics Department, University of California, Berkeley
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Abstract: The history of nonparametric inference is used to illustrate how a subdiscipline develops from isolated beginnings, both conceptually and through its dissemination via survey papers, lecture courses, and books.
2. Hydrodynamical Scaling and Large Deviations
Varadhan, S. R. S., New York University
Address: Mathematics Department, New York University
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Abstract: In general in probability theory, laws of large numbers are proved first, followed by fluctuation theory or central limit theorems and then the large deviation results are established. However in problems of hydrodynamical scaling, establishing even the laws of large numbers require a fair amount of ideas from large deviation theory. The lecture will consist of a description of what hydrodynamical scaling results are and why large deviation theory is important for proving them.
3. Applications of a Heuristic Concerning Partial Asymptotic Equivalence for Multivariate Estimation Problems
Brown, Lawrence D., University of Pennsylvania
Address: Statistics Department, University of Pennsylvania, Philadelphia, PA 19104-6302
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Email: lbrown@stat.wharton.upenn.edu
Abstract: Nonparametric function estimation problems include those usually described as nonparametric regression, density estimation, and signal processing. One dimensional versions of these problems have been proved under mild conditions to be asymptotically equivalent in a strong sense by Brown and Low and by Nussbaum (both in Ann. Statist., Dec. 1996). Consequently (under mild conditions), to any procedure in one setting there exist corresponding procedures in the others which have identical asymptotic properties.Multivariate versions of these problems present additional obstacles related to the curse of dimensionality. Consequently, multivariate extensions of the strong equivalence results mentioned above often require unpalatably strong smoothness conditions. (See Brown and Zhang, Ann. Statist., Feb. 1998.) In the present talk we will describe ways to use heuristics from the proof of the strong equivalence theorems in order to suggest weaker results about equivalence. These weaker results relate the asymptotic rates of convergence of appropriate procedures in the respective problems. Even in multivariate situations such partial results require only very mild conditions.
These ideas will be applied in the setting of multivariate tensor product models to derive some familiar and some new ratewise optimality results for appropriate smoothing spline estimators.
List of speakers who are nonmembers: