Award Abstract #9972417
Refined Approximation of Tail Probabilities, Expectation and Exponential Bounds for Partial Sums and Self-Normalized Martingales

NSF Org:	DMS Division of Mathematical Sciences
Initial Amendment Date:	August 2, 1999
Latest Amendment Date:	July 6, 2001
Award Number:	9972417
Award Instrument:	Continuing grant
Program Manager:	Dean M Evasius DMS Division of Mathematical Sciences MPS Directorate for Mathematical & Physical Sciences
Start Date:	August 15, 1999
Expires:	July 31, 2003 (Estimated)
Awarded Amount to Date:	$129600
Investigator(s):	Michael Klass jane@stat.berkeley.edu (Principal Investigator)
Sponsor:	University of California-Berkeley Sponsored Projects Office BERKELEY, CA 94704 510/642-8109
NSF Program(s):	PROBABILITY
Field Application(s):	0000099 Other Applications NEC
Program Reference Code(s):	OTHR,9260,0000
Program Element Code(s):	1263

ABSTRACT

The investigator plans to do work in two principal areas, sums and self-normalized sums. He (together with a co-author) intends to write up a very accurate result which can be applied to the approximation of tail probabilities of both real-valued and Banach space-valued partial sums of independent variates. Armed with certain functions defined from the marginal distributions of the variates, approximations of partial sum quantiles and p-th moments of great precision should follow. Secondly, the proposer (and co-authors) will address questions concerning exponential moment and tail probability upper bounds for self-normalized martingales. It is anticipated that statistical applications will occur as a consequence.

Probabilistic and statistical issues arise in a broad variety of theoretical and applied contexts. Most commonly the issues involve the probability of an event, the expectation of a random function, or a test of hypothesis. Real world applications of such results are wide-spread, extending from theory to data analysis in the social sciences, pharmaceuticals, finance, economics, engineering, the physical sciences, and the performance of algorithms. The investigator has worked in the area of sums of independent random variables for many years. He (together with co-authors) now is pursuing results of very refined precision. Included in this list are substantial improvements in the approximation of tail probabilities of partial sums and the location of their quantiles, expectation bounds, plus tail probability, exponential and moment generating function bounds for so-called self-normalized martingales.

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