Constructing estimators based on orthogonal components in a parametric model
Project/Area Number  10680325 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
Statistical science

Research Institution  The Institute of Statistical Mathematics 
Principal Investigator 
YANAGIMOTO Takemi The Institute of Statistical Mathematics, Department of Interdisciplinary Statistics, Professor, 領域統計研究系, 教授 (40000195)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥1,700,000 (Direct Cost : ¥1,700,000)
Fiscal Year 1999 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1998 : ¥1,200,000 (Direct Cost : ¥1,200,000)

Keywords  KullbackLeibler separator / Orthogonality / Simultaneous estimation / Logarithic link function / Stein estimator / 直交性 / 最尤推定量 / 推定方程式 / 対数線形回帰モデル / スタイン推定量 / 制約付最尤推定量 
Research Abstract 
The notion of orthogonality among components of a parameter is developed in relation with the estimation of the parameter. The promising situation are : 1) The dimension of a parameter high and 2) Distribution functions are parameterized in a favorable way. These restrictions may sound severely restrictive, but flexible models can be constructed in practice under this restriction. Among many interesting problems the present research focused on the two subjects ; the simultaneous estimation of a highdimensional mean parameter and the regression model with emphasis on the logarithmic link function. Several results relating the former subject were successfully obtained. In addition, a close relation with Bayesian approach has been called our attention. This finding will be significantly benefited for our subsequent researches. Specific results are concerned with 1) an unexpected application of the two estimating equation (to be appeared in SPL), 2) an application of the ordinal differential equation (to be appeared in CIS), 3) notions of orthogonality (Manuscript) and dual conjugate prior (in preparation). The three manuscripts except for the last are filed in the report of this research. Although we obtained some results on the latter subject of the regression model. The results are still below the satisfactory level. The present subject is obviously related with the most attractive subjects in both the theory and application of statistics. All the enthusiastic methods such as estimating equations, smoothing methods and separate inference are expected to owe the efficient use of the notion of orthogonality. It is my hope that the present research made a significant contribution on enhancing the research in this line.

Report
(4results)
Research Output
(14results)