Accurate estimation of the probability distribution of sample maximum and its applications

2022 Fiscal Year Final Research Report

• Project/Area Number: 19K20223
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 60030:Statistical science-related
• Research Institution: Tottori University
• Principal Investigator: Moriyama Taku 鳥取大学, 工学研究科, 助教 (30823190)
• Project Period (FY): 2019-04-01 – 2023-03-31
• Keywords: 極値理論 / セミパラメトリック推測 / ノンパラメトリック推測 / 確率分布推定 / 標本最大値

Outline of Final Research Achievements

This study considers the distribution estimation of sample maximum. I investigated the accuracies of two different estimators: the fitting estimator based on the extreme value theory and a nonparametric estimator as an alternative. It was found that the accuracy heavily depends on the tail index of the distribution. For distributions with the tail index around zero the nonparametric estimator outperforms the fitting estimator both theoretically and numerically, but the accuracy becomes very poor as the tail index gets far from zero. The accuracies of the two approaches are quite different. I developed the semiparametric approach that combines the two different approaches well and confirmed the numerical properties.

Free Research Field

統計科学

Academic Significance and Societal Importance of the Research Achievements

標本最大値は巨大リスクを考える際の1つの指標であり，これを正確に評価することは個々の問題の正確なリスクの把握を通じて，持続可能な社会を構築するのに不可欠である．本研究では，標本最大値の確率分布推定に対して，新たな高精度推定方法を確立した．ニューラルネットワークなどの活躍が目覚ましいなか，単純なノンパラメトリックモデルがうまく行かず，セミパラメトリックのような新たなアプローチの必要性を示すことができた点は統計学分野において学術的な意義がある．