|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)
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 simul
ation, 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.
データも基にEfton and Tibshirani(1993)のブートストラップ法,適合度検定,分布の探索法を使って頑健手法を選択するアルゴリズムを作成し,多くのモデルでの頑健統計手法のソフトプログラミングを行った。