Date: February 12-14, 2015

Venue: On February, 12, all the lectures will take place at the Steklov Mathematical Institute, Gubkina str. 8, Moscow, Russia. On February, 13-14, all the lectures will take place at the Faculty of Computational Mathematics and Cybernetics of Moscow State University, Leninskie Gory, 1/52, Moscow, Russia in aud. P-8a. Auditorium P-8a (П-8а) is located on the second floor in the northern part of the building. Numeration of the floors starts from zero.

“Probability Theory and its Applications” on Occasion of the 85-th Birthday of Yu.V.Prokhorov WEB SITE

Prof. Yasunori FUJIKOSHI attended “Probability Theory and its Applications” on Occasion of the 85-th Birthday of Yu.V.Prokhorov , which was held at the the Steklov Mathematical Institute and the Faculty of Computational Mathematics and Cybernetics of Moscow State University, from February 12 to 14.

Prof. Yasunori FUJIKOSHI of the SSRC had contributed his paper to the session.

Prof. Yasunori FUJIKOSHI of the SSRC had contributed his paper to the session.

**Title**:Explicit and Computable Error Bounds for Asymptotic Expansions of the Distribution Functions of Some Multivariate Statistics

**Abstract**:We are interested in two types of asymptotic approximations in multivariate analysis based on n samples of p variables. One is a large-sample asymptotic approximation under the case where n tends to infinity, but p is fixed. The other is a high-dimensional asymptotic approximation under the case where both p and p tend to infinity in a way such that p/n tends to c from [0; 1). Such asymptotic approximations have been obtained, see, e.g., Anderson (2003), Bai and Silverstein (2010), Fujikoshi et al. (2010), Muirhead (1982), Siotani et al. (1985). One side, the results on asymptotic approximations with explicit and computable error bounds are not so many. Some results have been obtained by using error bounds for approximations of the distributions of scale mixtures, multivariate scale mixtures and location and scale mixtures. Its systematic approach is given in Fujikosihi (1993), Fujikoshi et al. (2010). Some other error bounds have been obtained (see, e.g Wakaki (2008)) for high-dimensional approximations of LR statistics for covariance maricies whose moments are expressed in terms of gamma-functions. The purpose of the talk is to review results on explicit and computable error bounds in multivariate statistical analysis mensioned above and the recent results by Wakaki and Fujikoshi (2012) and Yamada et al. (2015).

**Day 1**

February 12(Thur.)

10:00-10:45

Opening Ceremony

10:45-11:30

Entropy Expansions in Probability

*Plenary Speaker: Friedrich Götze (Bielefeld University, Germany)*

11:30-11:45

Coffee-Break

11:45-12:30

Signatures

*Plenary Speaker: Narayanaswamy Balakrishnan (McMaster University, Canada)*

12:30-13:15

On Asymptotics and Estimates for Generalized Prokhorov Distance in Invariance Principle

*Plenary Speaker: Alexander Ivanovich Sakhanenko (Novosibirsk State University, Russia)*

13:15-14:45

Lunch

14:45-15:30

On Compactness of Families of Probability Measures on the Set of Quantum States

*Plenary Speakers: Maxim Evgen’evich Shirokov, Alexandr Semenovich Holevo (Steklov Mathematical Institute, Russia)*

15:30-16:15

Interaction and Limitation in Branching Processes

*Plenary Speaker: Peter Jagers (Chalmers University of Technology, Sweden)*

16:15-16:30

Coffee-Break

16:30-17:15

Large Intersecting Families in a Finite Set

*Plenary Speaker: Gyula O. H. Katona (Afréd Rényi Institute of Mathematics, Hungary)*

17:15-18:00

Inequalities for the Moments of Quadratic Forms

*Plenary Speaker:Alexander Nikolaevich Tikhomirov (Komi Scientific Center of Ural Branch of RAS, Russia)*

18:00-18:45

Prokhorov Memorial Lecture

*Plenary Speaker:Ernst L’vovich Presman (Central Economics and Mathematics Institute, Russia)*

19:00

Welcome reception

**Day 2**

February 13(Fri.)

10:00-10:45

On the Estimation of the Intensity Density Function of Poisson Random Field outside of the Observation Region

*Plenary Speaker:Il’dar Abdullovich Ibragimov (Steklov Institute of Mathematics, Russia)*

10:45-11:30

Risk Aggregation under Dependence Uncertainty

*Plenary Speaker:Paul Embrechts (ETH Zurich, Switzerland)*

11:30-11:45

Coffee-Break

11:45-12:30

Cramer Type Moderate Deviations of Normal and Non-normal Approximation

*Plenary Speaker:Qi-Man Shao (The Chinese University of Hong Kong, China)*

12:30-13:15

Least Energy Functions Accompanying Brownian Motion

*Plenary Speaker:Mikhail Anatolievich Lifshits (Saint Petersburg State University and Linköping University, Russia and Switzerland)*

13:15-14:45

Lunch

14:45-15:30

Invariance Principle and Probability Inequalities for Canonical von Mises’ Statistics of Dependent Observations

*Plenary Speaker:Igor’ Semenovich Borisov (Sobolev Institute of Mathematics, Russia)*

15:30-16:15

Asymptotic Theory for the Largest Eigenvalues of the Sample Autocovariance Function of High-Dimensional Heavy-Tailed Time Series

*Plenary Speaker:Thomas Mikosh (University of Copenhagen, Denmark)*

16:15-16:30

Coffee-Break

16:30-17:15

Explicit and Computable Error Bounds for Asymptotic Expansions of the Distribution Functions of Some Multivariate Statistics

**Plenary Speaker:Yasunori Fujikoshi (Hiroshima University, Japan)**17:15-18:00

Prokhorov’s Theorem and the Topology of Spaces of Probability Measures

*Plenary Speaker:Vladimir Igorevich Bogachev (Moscow State University, Russia)*

**Day 3**

February 14(Sat.)

10:00-10:45

Differences in Limit Theorems in Case of Normal or Non-Normal Stable Limit Distributions

*Plenary Speaker:Gerd Christoph (University of Magdeburg, Germany)*

10:45-11:30

Some Results Concerning the Sums of Independent Random Vectors Mathematics

*Plenary Speaker:Andrei Yurievich Zaitsev (Steklov Institute of Mathematics, Russia)*

11:30-11:45

Coffee-Break

11:45-12:30

Normal Mixture Models: Prokhorov’s Ideas and Some Recent Results

*Plenary Speaker:Victor Yurievich Korolev (Moscow State University, Russia)*

12:30-13:15

Continuity Problems in Boundary Crossing Problems

*Plenary Speaker:Konstantin Alexandrovich Borovkov (University of Melbourne, Australia)*

13:15-14:45

Lunch

14:45-15:30

Two-Dimensional Fused-Lasso with Non-Convex Penalty

*Plenary Speaker:Bing-Yi Jing (Hong Kong University of Science and Technology, China)*

15:30-16:15

Some Recent Results in the Field of Accuracy of the Normal Approximation to Sums of Independent Random Variables

*Plenary Speaker:Irina Gennadievna Shevtsova (Moscow State University, Russia)*

16:15-16:30

Coffee-Break

16:30-17:15

Generalized Renewal Processes. The Limit Behavior and Applications

*Plenary Speaker:Ekaterina Vadimovna Bulinskaya (Moscow State University, Russia)*

17:15-18:00

On Polynomials in Random Elements

*Plenary Speakers:Vladimir Vasilievich Ulyanov, Alexey Alexandrovich Naumov (Moscow State University, Russia)*

18:00

Closing Ceremony