ITLApplied  Computational Mathematics Division
ACMD Seminar Series
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Balanced Randomization Designs and Classical Probability Distributions

Andrew Rukhin
Information Technology Laboratory, Statistical Engineering Division; and University of Maryland, Baltimore County, Department of Mathematics and Statistics

Tuesday, February 3, 2004 15:00-16:00,
NIST North (820), Room 145
Tuesday, February 3, 2004 13:00-14:00,
Room 4550

Abstract: This talk compares the properties of the two most commonly used balanced randomization schemes with several treatments. Such sequential schemes are common in clinical trials, load balancing in computer file storage, etc. To force balance in an assignment between several treatments of sequentially arriving subjects, one has to choose a randomization design. One of the two following randomization schemes is commonly used in applications. The random allocation rule selects at random one out of the sequences which have exactly the prescribed number of subjects per treatment. The truncated multinomial design uses a randomization scheme which starts with the uniform probability assignment of subjects to treatments until one of the treatments receives its quota. Then the uniform distribution switches to the remaining treatments, and the allocation process continues in this way until there is just one treatment without its quota. This treatment then gets all remaining subjects. Formulas for the accidental bias and for the selection bias of both procedures are derived, and the large sample distribution of standard permutation tests is obtained. The limiting joint distribution of the moments at which a treatment receives the given number of subjects is discussed. The limiting behavior of the random allocation scheme is shown to be quite different from that of the truncated multinomial design. The relationship to classical probability distributions is discussed. These classical probability distributions involve the largest cell frequency in multinomial trials, the number of remaining matches in the Banach match-box problem, the birthday problem, and the number of vacant cells in the occupancy problem.

Speaker Bio: Andrew Rukhin received his M.S. in Mathematics (Honors) from the Leningrad State University (Russia) in 1967. In 1970 he defended his Ph.D. thesis in statistics at the Steklov Mathematical Institute. After emigrating from the USSR, he worked at Purdue University (1977-1987) and at University of Massachusetts, Amherst (1987-1989). Since 1989, Andrew Rukhin is a professor at the University of Maryland, Baltimore County. In 1994 he was appointed Mathematical Statistician in the Statistical Engineering Division, National Institute of Standards and Technology, where he is engaged in applied statistical research in Interlaboratory Studies, Statistical Decision Theory, Information Theory, Testing of Randomness, Bayesian Statistics, Change-Point Problems, Classification and Discrimination, Adaptive and Recursive Procedures, and Reliability Theory. Andrew is a Fellow of the Institute of Mathematical Statistics and a Fellow of the American Statistical Association. He won the Senior Distinguished Scientist Award from the Alexander von Humboldt-Foundation (1990) and the Youden Prize for Interlaboratory Studies (1998). He is also a Coordinating Editor of "Journal of Statistical Planning and Inference," and an Associate Editor of "Statistics and Probability Letters," of "Mathematical Methods of Statistics" (Executive Editor 1991-1995), and of "Applicationes Mathematicae."

Contact: P. M. Ketcham

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