Powers of a generalized least squares F test and an adjusted F test are studied under regression models with nested error structure.

Results on the analytic behavior of the limiting spectral distribution of matrices of sample covariance type, studied in Marcenko and Pastur [2] and Yin [8], are derived. Through an equation defining its Stieltjes transform, it is shown that the limiting distribution has a continuous derivative...

Suppose that we have (n - a) independent observations from Np(0, [Sigma]) and that, in addition, we have a independent observations available on the last (p - c) coordinates. Assuming that both observations are independent, we consider the problem of estimating [Sigma] under the Stein's loss...

Kiefer considered the asymptotics of q-sample Cramer-von Mises statistics for a fixed q and sample sizes tending to infinity. For univariate observations, McDonald proved the asymptotic normality of these statistics when q goes to infinity while the sample sizes stay fixed. Here we define a...

Tn the normal case it is well known that, although the James-Stein rule is minimax, it is not admissible and the associated positive rule is one way to improve on it. We extend this result to the class of the spherically symmetric distributions and to a large class of shrinkage rules. Moreover...

Confidence sets are constructed for the coefficients in a structural errors-invariables model with partial replication. These confidence sets are different from the traditional asymptotic confidence sets which have zero confidence levels, where the confidence level of a confidence set is defined...

In this paper we consider the problem of estimating the quadratic loss of point estimators of a location parameter for a family of spherically symmetric distributions. We compare the unbiased loss estimator of the minimax estimator with a new shrinkage type loss estimator. Conditions on the...

An algorithm is proposed and notions defined to determine the minimal sets of all possible higher order moments and cumulants of a random vector or a random matrix. The main attention has been paid to the case of symmetric matrices. Using the introduced notions, cumulants of arbitrary order for...

A general nonlinear regression model for repeated measures data is considered. Neyman's [16] partial score tests are derived for the significance of regression parameters as well as overdispersion components of the model. Neyman's score test is asymptotically locally optimal, and the test...

Under some mild conditions we establish Strassen's law of the iterated logarithm for the Lorenz curves.