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Seminar on Probability and Statistics
Seminar information archive ～04/19｜Next seminar｜Future seminars 04/20～
| Organizer(s) | Nakahiro Yoshida, Teppei Ogihara, Yuta Koike |
|---|
2020/05/01
17:00-18:10 Room #φ (Graduate School of Math. Sci. Bldg.)
Xiao Fang (Chinese University of Hong Kong)
High order distributional approximations by Stein's method (ENGLISH)
https://docs.google.com/forms/d/e/1FAIpQLSeSVwYsjhyQQXzjt3ZpvRh9ZEO5qZXxxLxYDYOu301Mc89RCA/viewform
Xiao Fang (Chinese University of Hong Kong)
High order distributional approximations by Stein's method (ENGLISH)
[ Abstract ]
Stein's method is a powerful tool to proving distributional approximations with error bounds. In this talk, we present two recent developments of Stein's method for high order approximations. (1) Together with Li Luo and Qi-Man Shao, we consider skewness correction in normal approximation. We prove a refined Cram¥'er-type moderate deviation result for a class of statistics possessing a local structure. We discuss applications to k-runs, U-statistics and subgraph counts. (2) Together with Anton Braverman and Jim Dai, we derive and justify new diffusion approximations with state-dependent diffusion coefficients for stationary distributions of Markov chains. We discuss applications to the Erlang-C system, a hospital inpatient flow model and the auto-regressive model.
[ Reference URL ]Stein's method is a powerful tool to proving distributional approximations with error bounds. In this talk, we present two recent developments of Stein's method for high order approximations. (1) Together with Li Luo and Qi-Man Shao, we consider skewness correction in normal approximation. We prove a refined Cram¥'er-type moderate deviation result for a class of statistics possessing a local structure. We discuss applications to k-runs, U-statistics and subgraph counts. (2) Together with Anton Braverman and Jim Dai, we derive and justify new diffusion approximations with state-dependent diffusion coefficients for stationary distributions of Markov chains. We discuss applications to the Erlang-C system, a hospital inpatient flow model and the auto-regressive model.
https://docs.google.com/forms/d/e/1FAIpQLSeSVwYsjhyQQXzjt3ZpvRh9ZEO5qZXxxLxYDYOu301Mc89RCA/viewform
