Budget Amount *help 
¥1,000,000 (Direct Cost : ¥1,000,000)
Fiscal Year 1999 : ¥400,000 (Direct Cost : ¥400,000)
Fiscal Year 1998 : ¥600,000 (Direct Cost : ¥600,000)

Research Abstract 
We considered twosample and multivariate twoway 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 pvariate continuous distribution function F(x,Σ) having null mean and finite positive definite variancecovariance matrix Σ. In pratical applicational model assumptions, the scaleparameter 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 Mstatistics were proposed. Their asymptotic noncentral xィイD12ィエD1distributions for testing homogeneity were drawn under a contiguous sequence of locationalternatives 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 Mtest 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 Mstatistics. The asymptotic normality of these estimators was drawn. After a simple algorithm was studied, the risks of the Mestimators 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 Mprocedures relative to parametric procedures agreed with the ARE of onesample Mestimator proposed by Huber (1964) relative to the sample mean, and that (ii) for small sample sizes, the Mprocedures 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.
