1990 Fiscal Year Final Research Report Summary
A Study on Asymptotic Methods for Statistical Inference
| Project/Area Number |
01540181
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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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, 基礎工学部, 教授 (10000184)
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| Co-Investigator(Kenkyū-buntansha) |
TANIGUCHI Masanobu Osaka University, Engineering Science, Ass. Prof., 基礎工学部, 助教授 (00116625)
SHIRAHATA Shingo Osaka University, General Education, Professor, 教養部, 教授 (10037294)
DATE Etsurou Osaka University, Engineering Science, Professor, 基礎工学部, 教授 (00107062)
FUKUSHIMA Masatoshi Osaka University, Engineering Science, Professor, 基礎工学部, 教授 (90015503)
ISII Keiiti Osaka University, Engineering Scinece, Professor, 基礎工学部, 教授 (80029420)
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| Project Period (FY) |
1989 – 1990
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| Keywords | Parametric Models in Stochastic Processes / Likelihood Analysis / General Linear Models / Maximum Likelihood Estimator / Nonparametrics / Robustness / Quasi-Likelihood Function / Time Series |
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| Research Abstract |
AIM : Our aim of this study is to investigate the mathematical structure of estimation and test in statistical inference by the asymptotic behavior of likelihood function of parametric models, and especially, to investigate the asymptotic structure of new parametric models in stochastic process. In the case of nonparametric models, we treat estimators and test statistics written down as functionals of empirical distribution function and investigate those asymptotic properties by properties of integrals of Wiener measure.
PLAN : Our plan of this study is as follows : (1) INAGAKI studies the relationship between the differentiability and asymptotic expansion of the likelihood function, especially, in the parametric models of stochastic processes. (2) INAGAKI and MATSUO study the roles of link functions and quasilikelihoods in the general linear regression model, which is useful in Application Statistics.
(3) SHIRAHATA studies the asymptotic methods in nonparametric models and evaluates the
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performance of them by simulation experiments. (4) TANIGUCHI investigates the robustness in the time series analysis, which is recently developed. (5) ISII, FUKUSHIMA and DATE study the mathematical foundation of the asymptotic theory of statistical inference.
RESULTS : Our results of this research project are as follows : (1) INAGAKI published a book "STATISTICAL MATHEMATICS" (in Japanese) in section "LIKELIHOOD ANALYSIS" of which the role of likelihood function is expressed for the asymptotic theory of estimation and test. Also, he read a paper "simple self-correcting point processes with several levels" at the annual meeting (1990) of the MATHEMATICAL SOCIETY of JAPAN. (2) MATSUO published a paper about the general linear regression model. (3) SHIRAHATA submitted a paper with respect to the convergence of multidimensional empirical distribution function. (4) TANIGUCHI submitted a paper about the robustness in time series analysis. (5) FUKUSHIMA and DATE published papers of mathematical foundations of the asymptotic theory.
Reconsideration : Our study stimulates researches about asymptotic theory of the statistical inference, especially for parametric model of stochastic processes, which is recently developed. These studies should be verified the utility and ability in statistical applications. Less
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