2004 Fiscal Year Final Research Report Summary
A STUDY ON STATISTICAL INFERENCE OF STOCHASTIC PROCESS AND ITS ROBUSTNESS
| Project/Area Number |
14540115
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | OSAKA UNIVERSITY |
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Principal Investigator |
INAGAKI Nobuo OSAKA UNIVERSITY, ENGINEERING SCIENCE, PROFESSOR, 大学院・基礎工学研究科, 教授 (10000184)
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| Co-Investigator(Kenkyū-buntansha) |
SHIRAHATA Shingo OSAKA UNIVERSITY, ENGINEERING SCIENCE, PROFESSOR, 大学院・基礎工学研究科, 教授 (10037294)
KANO Yutaka OSAKA UNIVERSITY, ENGINEERING SCIENCE, PROFESSOR, 大学院・基礎工学研究科, 教授 (20201436)
KUMAGAI Etsuo OSAKA UNIVERSITY, ENGINEERING SCIENCE, LECTURER, 大学院・基礎工学研究科, 講師 (20273617)
AKI Shigeo KANSAI UNIVERSITY, ENGINEERING, PROFESSOR, 工学部, 教授 (90132696)
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| Project Period (FY) |
2002 – 2004
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| Keywords | Statistical inference of stochastic processes / Exponential stochastic processes / Likelihoods of stochastic processes / Convex analysis of likelihood functions / Likelihoods of diffusion processes / Ornstien-Uhlenbeck process / Robust inferenceof stochastic process / Bivariate random processes |
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| Research Abstract |
Our aim of this study is to investigate the statistical inference of stochastic processes by their likelihood functions, especially for "exponential" stochastic processes and furthermore, to investigate the robust statistical inference for observations with additive outliers. The important mathematical structure of statistical inference is discussed by using the statistical informations in exponential stochastic processes.
Our plan of this study is as follows :
(1) We study the likelihood function of parametric models of stochastic process, especially exponential stochastic processes, and their statistical informations by the stochastic integral and Ito's formula.
(2) We investigate 'the relationship between the statistical curvature and the information loss.
(3) We study asymptotic methods in nonparametric and semi-parametric models and evaluates the performance of them by simulation experiments.
(4) We study the first occurrence time of run and pattern in dependent sequence of bivariate observations.
Our results of this research project are as follows :
(1) We published the revise of "Mathematical Statistics" (in Japanese).
(2) We write a paper "Exact information loss in multivariate gamma distribution" at Scientiae Mathematicae Japonicae (SCMJ) (2005).
(3) We published a paper about a selection of models (2005) in press.
(4) We write several papers about distributions of runs and patterns in dependent processes.
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