The Grassmann manifold Gk,m - k consists of k-dimensional linear subspaces in Rm. To each in Gk,m - k, corresponds a unique m - m orthogonal projection matrix P idempotent of rank k. Let Pk,m - k denote the set of all such orthogonal projection matrices. We discuss distribution theory on Pk,m -...

We consider the competing risks model with grouped data or with discrete Failure times where a unit is exposed to several risks, but its eventual failure is due to exactly one of the causes. Nonparametric maximum likelihood estimates of the cause specific hazard rates are obtained under the...

The problem of deriving robust and classically acceptable Bayesian inference on location parameters is considered in this paper. The main result of the paper allows one to obtain uniform posterior approximation starting with likelihood functions with heavy tails, e.g., t-distributions with...

Studying the joint distributional properties of partial sums of independent random variables, we obtain stochastic analogues of some simple deterministic results from the theory of majorization, Schur-convexity, and arrangement monotonicity. More explicitly, let Xi([theta]i), i =1, ..., n, be...

Let ..., X-1, X0, X1, ... be symmetric i.i.d. random variables belonging to the domain of normal attraction of an [alpha]-stable distribution with 1 [alpha] 2, and let cj = j-[beta][Lambda](j) with 1/[alpha] [beta] and a slowly varying [Lambda](j). We study the limit behavior of the partial...

The asymptotic distribution of k th nearest neighbor regression and autoregression estimates (local means) is obtained for [alpha]-mixing processes. Local medians, as considered by Truong and Stone (1991, Ann. Statist.20 77-97), are also shown to be asymptotically normally distributed.

The paper presents a procedure for testing a general multivariate distribution for symmetry about a point and, also, a procedure adapted to the special properties of multivariate stable laws. In the general case use is made of a stochastic process derived from the empirical characteristic...

In this paper a theorem on gambling systems for Bernoulli sequences is extended to arbitrary binary random sequences by using the notion of the likelihood ratio, and an analytical technique for the study of a.e. convergence is presented.

Under the i.i.d. condition, Marron and Härdle (1986, J. Multivariate Anal.20 91-113) showed that quadratic measures of errors for nonparametric kernel estimates are asymptotically equivalent, and Hall (1984, J. Multivariate Anal.14 1-16) investigated their convergence rates. In this article, we...

In balanced mixed linear models it is often possible to estimate the treatment means and the variance components with UMV estimators. In two instances, the mixed two-way classification model and the split-plot model, it is shown that the UMV estimator of the treatment mean vector is inadmissible...