Studentized robust statistics for,main effects in a two-factor manova

Multiresponse experiments in two-faoior manova are considered. StalibLical procedures of the test and estimation, based on studentized robust statistics. for location parameters in the models arc piupused. Large sample properties of their procedures as the cell sizes tend to infinity are investigated. Although Fisher's consistency is assumed in the theory ol ili-estimators, it is not needed. in this paper. For the univariate case, it is found that the asymptotic relative efficiencies (ARE's) of the proposed procedures relative to classical procedures agrees with the classical A/Sisresults of Huber's one sample Mestimator relative to the sample mean. By simulation studies, it can be seen that the proposed estimators are more efficient than the least squares estimators except for the case where the underlying distribution is normal     

Improved estimation for the autocovariances of a Gaussian stationary process

For a Gaussian stationary process with mean μ and autocovariance function γ(·), we consider to improve the usual sample autocovariances with respect to the mean squares error (MSE) loss. For the cases μ=0 and μ≠0, we propose sort of empirical Bayes type estimators Γ? and Γ?, respectively. Then their MSE improvements upon the usual sample autocovariances are evaluated in terms of the spectral density of the process. Concrete examples for them are provided. We observe that if the process is near to a unit root process the improvement becomes quite large. Thus, consideration for estimators of this type seems important in many fields, e.g., econometrics.     

Closed testing procedures for all pairwise comparisons in a randomized block design

We consider multiple comparison test procedures among treatment effects in a randomized block design. We propose closed testing procedures based on maximum values of some two-sample t test statistics and based on F test statistics. It is shown that the proposed procedures are more powerful than single-step procedures and the REGW (Ryan/Einot–Gabriel/Welsch)-type tests. Next, we consider the randomized block design under simple ordered restrictions of treatment effects. We propose closed testing procedures based on maximum values of two-sample one-sided t test statistics and based on Batholomew’s statistics for all pairwise comparisons of treatment effects. Although single-step multiple comparison procedures are utilized in general, the power of these procedures is low for a large number of groups. The closed testing procedures stated in the present article are more powerful than the single-step procedures. Simulation studies are performed under the null hypothesis and some alternative hypotheses. In this studies, the proposed procedures show a good performance.     

Testing homogeneity against trend based on rank in one-way layout

In this paper, we are concerned with testing homogeneity against trend. Parsons (1979) considered the exact distribution of the test statistic based on the Wilcoxon type scores. We extend his result to the case of the general scores. Then we give a table of significance probabilities for the Fisher-Yates normal scores. We also study the asymptotic distribution of the test statis-tic based on the general scores under the null hypothesis, and the asymptotic relative efficiency against Bartholomew's likelihood ratio test assuming normality