ИНФОРМАЦИЯ О БОЛЬШОМ СЕМИНАРЕ
КАФЕДРЫ ТЕОРИИ ВЕРОЯТНОСТЕЙ
(руководитель - член-корр. РАН, профессор А.Н. Ширяев)

Программа на сентябрь 2008 г.

24 сентября.

H. Wakaki (Hiroshima University). An error bound for Box's chi-square type asymptotic expansion of Wilks' Lambda distribution.

Abstract.
An error bound for the Box's chi-square type asymptotic expansion of Wilks' Lambda distribution is derived. It is compared with an error bound for the high-dimensional Edgeworth expansion.

T. Akita (Hiroshima University). An Improvement Method of Sliced Inverse Regression using Principal Component Analysis.

Abstract.
We suggest an improvement method of sliced inverse regression (SIR) which is called gPCA-SIR h. The idea of the method is re-separating the group of the data, which is separated in some slices of the response variable, by using principal components. We also compare SIR with PCA-SIR by simulation, and prove the convergence of estimator.

Zh. Assylbekov (Hiroshima University). Convergence of Multinomial Goodness-of-fit Statistics to Chi-square Distribution.

Abstract.
Let Y=(Y1, Y2,..., Yk)' be a random vector with multinomial distribution. In the talk we investigate the convergence rate of so-called power divergence family of statistics {Iλ(Y), λÎR}, introduced by Cressie and Read (1984) to chi-square distribution. It is proved that for every k³4

Pr(2n Iλ(Y) <c)=Gk-1(c)+O(nm(k-1)-1),

where Gr(c) is the distribution function of chi-square random variable with r degrees of freedom, m(r)=6/(7r +4) for 3£r£7, m(r)=5/(6r+2) for r³8. This refines Zubov and Ulyanov's result (2008). The proof uses Kratzel-Nowak's theorem (1991) on the number of integer points in a convex body with smooth boundary.

Координатор Большого кафедрального семинара на осенний семестр 2008 года - к.ф.-м.н. Селиванов Андрей Валерьевич (e-mail: selivanov.andrey@gmail.com).

Ученый секретарь Большого кафедрального семинара на осенний семестр 2008 года - Абакирова Айгуль Тилековна (e-mail: abakirova@gmail.com).