2015년 제4회 통계세미나 개최 안내
통계연구소에서는 다음과 같이 통계 세미나를 개최하오니 많은 참여 바랍니다.
일시: 2015년 5월 28일 (목) 오후 5시
장소: 고려대학교 정경관 506호
연사: 김경희 박사 (University of Cambridge)
Adaptive and minimax optimal estimation of the tail coefficient, and
associated adaptive and honest confidence sets
A fundamental problem in extreme value theory is to estimate the tail coefficient (or the first order parameter), since it characterises the nature of the extreme events. In this talk, I will first present an alternative estimator of the tail index. This estimator is minimax-optimal, under the assumption that the model satisfies a second order Pareto type condition. Moreover, an adaptive version of this estimate adapts to the second order parameter, and achieves a rate that is minimax optimal simultaneously on all models. I will then discuss the problem of providing a confidence set for the tail coefficient. Confidence set problem is linked to the problem of testing the complexity of the model, i.e. it is translated into a composite testing problem. I will propose a solution to this problem. This presentation is based on two papers: (1) Adaptive and minimax optimal estimation of the tail coefficient and (2) Adaptive confidence intervals for the tail coefficient in a wide second order class of Pareto models. Both are joint work with Alexandra Carpentier.
Keywords: Adaptive estimation, minimax optimal bounds, extreme value index, Pareto-type distributions, testing
고려대학교 통계연구소