McMASTER UNIVERSITY STATISTICS SEMINAR

Week of September 18 - 22, 2000

SPEAKER:	S. G. Mohanty McMaster University
TITLE:	"Historical up-and-down designs for quantile estimation"
DAY:	Monday, September 18, 2000
TIME:	4:00 p.m. [Coffee & cookies in BSB-202 at 3:30 p.m.]
PLACE:	BSB-B103

SUMMARY

In a dose-response study, biased coin designs which are variations of an up-and-down rule have been considered for estimating a quantile, the unknown dose corresponding to a fixed probability of response. These rules are sequential in nature in which allocation of the dose level for the next trial is based on the outcome of the current trial. Another rule as proposed by Johnson and Narayana in which the allocation of the dose level depends on the outcomes of all trials on the level of the current trial. In both cases the selection of levels is restricted to one level higher, one level lower or the same. The Johnson-Narayana rule defines a design which may be called a historical up-and-down design. By using extensive simulation, comparisons of this design with biased coin designs and of different estimators are made. In addition, a few other questions are studied.

Joint work with S. Durham (The University of South Carolina, SC) and A.A. Montazer-Haghighi (Benedict College, SC)

ABOUT THE SPEAKER

Sri Gopal Mohanty received his B.A. from Utkal University, his M.A. from Panjab University, and his Ph.D. from the University of Alberta. He is now Professor Emeritus of Mathematics and Statistics at McMaster University. His research interests include random walks, queues, nonparametric inferences, discrete distributions, and enumerative combinatorics.

REFERENCES

The references below, suggested by the speaker as useful background for this talk, have been placed on reserve at Thode Library (STATS 770: Statistics Seminar).

Durham, S.D. & N. Flournoy (1994) Random walks for quantile estimation. In Statistical Decision Theory and Related Topics V, S.S. Gupta & J.O. Berger (eds), pp 467-476. New York: Springer-Verlag.

Durham, S.D., N. Flournoy & A.A. Montazer-Haghighi (1993) Up-and-down-designs. In Computing and Statistics: Interface 23, M.E. Tarter & M.D. Lock (eds), pp 375-384.