Novel tools of statistical analysis via their algebraic properties

2015 Fiscal Year Final Research Report

• Project/Area Number: 24700288
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Statistical science
• Research Institution: The Institute of Statistical Mathematics
• Principal Investigator: Kobayashi Kei 統計数理研究所, 大学共同利用機関等の部局等, 助教 (90465922)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 代数統計学 / 漸近統計学 / 情報幾何学 / 高次元データ解析

Outline of Final Research Achievements

A class of novel algebraic estimators for algebraic models is proposed. We proposed an explicit method to compute the estimators and estimates by using computational algebraic methods. The estimators are defined by some lower-degree polynomial equations by holding some asymptotic statistical efficiency. This allows fast computation of the estimates. This research should be the first result evaluating and controlling trade-off between algebraic computation and statistical efficiency. Another result is a new permutation test for dendrograms by using their geometrical and algebraic structures. We tested difference between mental lexicons between groups of examinees by using the proposed method. The results of this research project have been published in several international conferences and journals.

Free Research Field

統計科学