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 15:0016:00, NIST North (820), Room 145 Gaithersburg Tuesday, February 3, 2004 13:0014:00, Room 4550 Boulder
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 matchbox 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 (19771987) and
at University of Massachusetts, Amherst (19871989).
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, ChangePoint 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 HumboldtFoundation (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 19911995),
and of "Applicationes Mathematicae."
Contact: P. M. KetchamNote: Visitors from outside NIST must contact
Robin Bickel; (301) 9753668;
at least 24 hours in advance.
