| Project/Area Number |
04630014
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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 |
Economic statistics
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| Research Institution | Institute of Economic Research, Hitotsubashi University |
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Principal Investigator |
KARIYA Takeaki Hitotsubashi Univ.Inst.of Economic Research Professor, 経済研究所, 教授 (70092624)
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| Project Period (FY) |
1992 – 1993
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| Project Status |
Completed (Fiscal Year 1993)
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| Budget Amount *help |
¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 1993: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1992: ¥700,000 (Direct Cost: ¥700,000)
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| Keywords | Test for Multivariate Normality / Test for Gaussianity / Curved Family / Locally Best Invariant Test / Mardia's Test / 多変量光度 / ガウス性の検定 / エルミート多項式 / 多変量正規性の検定 / 曲分布族 |
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| Research Abstract |
In a view of testing multivariate normality, a new testing procedure for testing the Gaussianity of stationary time series process is proposed. The basic idea is that first standardizing p variates and then transforming them by Hermitian polynomials, the moment structure of the p-dim. multivariate normality is tested based on the transformed variates. The test statistic is shown to be asymptotically distributed as x^2-distribution. These results are applied to testing the Gaussianity of a univariate time series by considering lagged variates p-dim variates. The method is applied to returns of stocks and the Gaussianity is rejected.
Also the problem of testing multivariate normality against a curved family is treated and the locally best invariant test and its distribution are derived. A curved family for which the Mardia test is locally best invariant is found.
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