A study on statistical inference and survival analysis based on algebraic and geometric structures

2022 Fiscal Year Final Research Report

• Project/Area Number: 20K19752
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 60030:Statistical science-related
• Research Institution: The University of Tokyo
• Principal Investigator: OGAWA Mitsunori 東京大学, 大学院情報学環・学際情報学府, 特任講師 (50758290)
• Project Period (FY): 2020-04-01 – 2023-03-31
• Keywords: 統計的推測 / ダイバージェンス / バイアス補正 / 推定値の存在性

Outline of Final Research Achievements

We studied the problem of estimating the structural parameter of discrete exponential family models under the presence of nuisance parameters based on the composite local Bregman divergences on the conditional distributions obtained by conditioning sufficient statistics for the nuisance parameters. In particular, we developed estimation methods with a certain robustness property.
We also studied the existence of estimates for Firth's bias-correction method in logistic regression models. We proved the existence of the estimates in the binomial logistic regression case, while we found a counterexample for the discussion of previous research in the multinomial logistic regression case.

Free Research Field

統計学

Academic Significance and Societal Importance of the Research Achievements

局外パラメータを含む統計モデルの推測手法の開発は統計学における古典的問題であり，特に計算負荷の軽減と統計的性質の両方をあわせもつ手法の開発には意義がある．本研究で用いた枠組みは近年の代数統計とダイバージェンスに基づく方法の両者の利点を活用したものであり，学術的にも意義あるものと考える．Firthのバイアス補正推定値の存在性に関する研究は，複数の応用領域において理論保証が不十分なまま普及している利用方法を検証するものであり，理論と応用の両面から意義あるものである．