外国人訪問研究者による講演会のお知らせ
題目『On approximation of goodness-of-fit statistics for discrete multivariate data』
講演者Vladimir V. Ulyanov先生(モスクワ大学数学科)
日時:2008年2月1日(金)15:00~16:30
会場:後楽園キャンパス6号館7階6701
We study approximation for power-divergence family
of statistics which includes in particular traditional
goodness-of-fittests: Pearson'schi-square test, loglikelihood
ratio statistic andFreeman-Tukey statistic.
We get rate of convergence to chi-square distribution
reducing the original problem to problem of approximation
of number of lattice points in large convex bodies.
The talk consists of two parts: at first we consider
approximation for Pearson's chi-square test. It leads to
classical problem in number theory about number of integer
points in ellipsoids.
The second partis devoted to other statistics whose distribution
functions could be represented as probabilities that normed sums
of independentinteger valued random vectors hit convex sets
which are "similar" to ellipsoids. In this case it is necessary to
apply number theoretic results obtained just recently.