The clarification of non-regular structure in statistical inference and its applications

2015 Fiscal Year Final Research Report

• Project/Area Number: 23340022
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: University of Tsukuba
• Principal Investigator: Akahira Masafumi 筑波大学, 名誉教授 (70017424)
• Co-Investigator(Kenkyū-buntansha): AOSHIMA Makoto 筑波大学, 数理物質系, 教授 (90246679) ; KOIKE Ken-Ichi 筑波大学, 数理物質系, 准教授 (90260471) ; OHYAUCHI Nao 筑波大学, 数理物質系, 助教 (40375374) ; TORIGOE Norio 東海大学, 理学部, 准教授 (40297180)
• Project Period (FY): 2011-04-01 – 2016-03-31
• Keywords: 切断分布族 / 最尤推定 / 漸近展開 / 漸近損失

Outline of Final Research Achievements

In the research, in the non-regular case when regularity conditions do not necessarily hold, the aim was to clarify the non-regular inferential structure from the viewpoint of higher order asymptotic expansion. For a one-/two-sided truncated exponential family of distributions as a typical non-regular family, an estimation problem on a natural/truncation parameter was considered. In the estimation of a natural parameter when a truncation parameter was a nuisance one, the asymptotic expansions of the maximum likelihood estimator (MLE)(0) of a natural parameter when a truncation parameter was known and the bias-adjusted MLE(1) of a natural parameter when a truncation parameter was unknown were derived, their asymptotic variances were obtained, and the second order asymptotic loss of MLE(1) relative to MLE(0) was given. The MLE of a truncation parameter when a natural parameter was a nuisance one was also considered. From the result the non-regular structure was clarified.

Free Research Field

数理統計学