1999 Fiscal Year Final Research Report Summary
Statistical interence based on studentized robust statistics
| Project/Area Number |
10640129
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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 | Yokohama City University |
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Principal Investigator |
SHIRAISHI Takaaki Department of Mathematical Sciences Associate Professor, 理学部, 助教授 (50143160)
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| Co-Investigator(Kenkyū-buntansha) |
ICHIRAKU Shigeo Department of Mathematical Sciences Professor, 理学部, 教授 (30046130)
KONNO Yoshihiko Chiba University Institute of natural science Associate Professor, 大学院・自然化学研究科, 助教授 (00205577)
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| Project Period (FY) |
1998 – 1999
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| Keywords | robustness / asymptotic theory / analysis of variance / bootstrap / permutation tests / simulation / computer programming |
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| Research Abstract |
We considered two-sample and multivariate two-way manova model included in YィイD2iィエD2=h(xィイD2iィエD2,θ) + εィイD2iィエD2, i=1,・・・, n,θ∈Θ where εィイD2iィエD2, i=1, ・・・, n, are mutually independent and identically distributed with a p-variate continuous distribution function F(x,Σ) having null mean and finite positive definite variance-covariance matrix Σ. In pratical applicational model assumptions, the scale-parameter of the underlying distribution is unknown and Fisher's consistency does not hold. We need to construct flexible statistical procedures. So scale invariant statistical procedures based on M-statistics were proposed. Their asymptotic noncentral xィイD12ィエD1-distributions for testing homogeneity were drawn under a contiguous sequence of location-alternatives without assuming Fisher consistency : ∫ψィイD2lィエD2(xィイD1(l)ィエD1)dFィイD2lィエD2(xィイD1(l)ィエD1)=0. Asymptotic robustness was derived. The permutation tests based on the proposed M-test statistics were considered. Using a Monte Carlo simulation, their power was compared with permutation tests based on parametric test statistics. Next robust estimators for location parameters were proposed, based on studentized M-statistics. The asymptotic normality of these estimators was drawn. After a simple algorithm was studied, the risks of the M-estimators and the least squares estimators were compared due to a simulation. For a univariate case, it was found that (i) the asymptotic relative efficiency (ARE) of the proposed M-procedures relative to parametric procedures agreed with the ARE of one-sample M-estimator proposed by Huber (1964) relative to the sample mean, and that (ii) for small sample sizes, the M-procedures were more efficient than parametric procedures except the case that an underlying distribution is normal.
Moreover many computer soft programs were created and shrinkage estimators were discussed.
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