2001 Fiscal Year Final Research Report Summary
A STUDY ON ASYMPTOTIC STRUCTURE OF STATISTICAL INFERENCE FOR PARAMETRIC MODELS OF STOCHASTIC PROCESS
| Project/Area Number |
11640117
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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) |
TANIGUCHI Masanobu OSAKA UNIVERSITY, ENGINEERING SCIENCE, ASSOC. PROF., 大学院・基礎工学研究科, 助教授 (00116625)
ISOGAI Takafufumi OSAKA UNIVERSITY, ENGINEERING SCIENCE, ASSOC. PROF., 大学院・基礎工学研究科, 助教授 (00109860)
SHIRAHATA Shingo OSAKA UNIVERSITY, ENGINEERING SCIENCE, PROFESSOR, 大学院・基礎工学研究科, 教授 (10037294)
KUMAGAI Etsuo OSAKA UNIVERSITY, ENGINEERING SCIENCE, ASSIST. PROF., 大学院・基礎工学研究科, 助手 (20273617)
AKI Shigeo OSAKA UNIVERSITY, ENGINEERING SCIENCE, ASSOC. PROF., 大学院・基礎工学研究科, 助教授 (90132696)
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| Project Period (FY) |
1999 – 2001
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| Keywords | PARAMETRIC MODELS IN STOCHASTIC PROCESSES / LIKELIHOOD AND QUASI-LIKELIHOOD FUNCTION OF STOCHASTIC PROCESSES / EXPONENTIAL FAMILY OF DISTRIBUTIONS / GENERAL LINEAR MODELS / MAXIMUM LIKELIHOOD ESTIMATOR AND ITS ASYMPTOTIC PROPERTIES / EXPONENTIAL STOCHASTIC PROCESS AND STATISTICAL INFERENCE / ROBUSTNESS IN TIME SERIES ANALYSIS / GIOSTATISTICS AND KRIGING |
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| Research Abstract |
AIM : Our aim of this study is to investigate the mathematical structure of statistical inference by the asymptotic behavior of likelihood functions of parametric models of stochastic process and especially, to investigate the likelihood functions of "exponential"stochastic processes and their asymptotic properties. The important mathematical structure of statistical inference is discussed by using asymptotic properties of the statistical informations in exponential stochastic processes.
PLAN : Our plan of this study is as follows: (1) INAGAKI studies 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) INAGAKI and KUMAGAI investigate the asymptotic relationship between the statistical curvature and the information loss by which they give the charicterization of Efron's parametrization. (3) SHIRAHATA studies the asymptotic methods in nonparamet
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ric and semi-parametric models and evaluates the performance of them by simulation experiments. (4) TANIGUCHI investigates the robustness in the time series analysis. (5) AKI studies the first occurrence time of run and pattern in dependent sequence, such as Markov dependent trials and sampling from urn models.
RESULTS : Our results of this research project are as follows: (1) INAGAKI published a book "FOUNDAMENTALS OF STATISTICS" (in Japanese) with other two coauthors. (2) INGAKI and KUMAGAI write a paper "On Efron's parametrization" at Australian ＆ New Zealand Journal os Statistics (2002) (in press) with another coauthor. (3) SHIRAHATA published a paper about the response ratios of each quation in sampling quationnaire. (4) TANIGUCHI writes a paper about the robustness in time series analysis. TANIGUCH and KAKIZAWA published a book "Asymptotic Theory of Statistical Inference for Time Series" Springer, Verlag, New York. (5) AKI writes several papers about distributions of runs and patterns in dependent processes. Less
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