| Project/Area Number |
63530009
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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 |
統計学
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| Research Institution | HITOTSUBASHI UNIVERSITY |
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Principal Investigator |
HAYAKAWA Takesi Hitotsubashi University, Department of Economics, Professor, 経済学部, 教授 (00000183)
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| Co-Investigator(Kenkyū-buntansha) |
HAYAKAWA Takesi Hitotsubashi University, Department of Economics Professor (00000183)
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| Project Period (FY) |
1988 – 1989
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| Project Status |
Completed (Fiscal Year 1989)
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| Budget Amount *help |
¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 1989: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1988: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Keywords | Langevin population / Likelihood ratio criterion / Wald statistic / Watson statistic / Discriminant analysis / Misclassification / Plug-in statistic / Rao statistic / Langerin分布 / Wald統計量 / Plug-In統計量 / Rao統計量 / 誤判別確率 / 検出力 / Langevin分布 / 改良Wald統計量 / Elliptical母集団 / F-集団 / 固有値 |
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| Research Abstract |
This research studied the following problems. (1) Tests of parameters (mean direction and concentration parameter) of Langevin population on a sphere. Test statistics (Likelihood ratio criterion, Watson statistic, Wald statistic, Rao statistic etc.) are proposed and asymptotic expansions of the distributions of these are obtained. The simulation experiments show that the asymptotic expansions give good agreements with simulation results. (2) The discriminant functions (Plug-In statistic and Likelihood ratio criterion) for two Langevin populations are proposed. The comparison of these in done from theoretical and simulational points of view. (3) The survey was done for the recent development of zonal polynomials and invariant polynomials which are fundamental ones for the study, of the distributional problems in multivariate analysis.
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