Spherical regression in a decision theoretic framework is examined, where the data is observed on S2 with the parameter space being SO(3). Bayes estimators are characterized under squared error loss on SO(3) as well as conditions under which the least squares estimator is a Bayes estimator with...

The paper considers estimation of matrix normal means. A class of empirical Bayes estimators is proposed which dominates the maximum likelihood estimator simultaneously for many quadratic losses. Several of these empirical Bayes estimators are compared in terms of their simulated risks, and a...

A class of new parametric models on the unit simplex in Rm is introduced, the distributions in question being obtained as conditional distributions of m independent generalized inverse Gaussian random variables given their sum. The Dirichlet model occurs as a special case. Two other special...

We propose a random censorship model which permits uncertainty in the cause of death assessments for a subset of the subjects in a survival experiment. A nonparametric maximum likelihood approach and a "self-consistency" approach are considered. The solution sets corresponding to both approaches...

Conditions are investigated which imply the tightness of certain weighted sums [Sigma]i = 1kn aniXi of random functions (Xn) taking values in D([0, 1]; E), where E is a separable Banach space. Improved weak laws of large numbers result as corollaries. Examples are presented to clarify the...

Regression quantiles provide a natural and powerful approach for robust analysis of the general linear model. However, departures from independence and stationarity of the errors can have an extremely potent effect on statistical analysis. Here, a Bahadur representation for regression quantiles...

In a linear model Y = X[beta] + Z a linear functional [beta] -- [gamma]'[beta] is to be estimated under squared error loss. It is well known that, provided Y is normally distributed, the ordinary least squares estimation function minimizes the risk uniformly in the class of all equivariant...

We discuss rates of convergence for the distribution of normalized sample extremes to the appropriate limit distribution. We show that the rate of convergence depends on that of the corresponding dependence functions and that of the marginals. The univariate results are well known by now, so we...

For Xi, ..., Xn a random sample and K(·, ·) a symmetric kernel this paper considers large sample properties of location estimator satisfying , . Asymptotic normality of is obtained and two forms of interval estimators for parameter [theta] satisfying EK(X1 - [theta], X2 - [theta]) = 0, are...

A generalized Cramér-Rao analogue for median-unbiased estimators having continuous joint density functions is given by defining a dispersion measure, joint diffusivity, analogous to the generalized variance in mean-unbiased estimation and extending the usual definition of median-unbiasedness to...