We introduce M-estimators for location and concentration parameters of von Mises-Fisher distributions on unit spheres. These include the directional mean, normalized spatial median, spherical median, and the mle of the concentration parameter. We find the influence functions and asymptotic...

Let {xt} (t = 0, ±1, ±2, ...) be a linear process, xt = [epsilon]t + b(l) [epsilon]t - 1 + · · ·, where {[epsilon]t} is a sequence of independent identically distributed random variables with the common distribution in the domain of attraction of a symmetric stable law of index...

A mixed distributional limit theorem for a stable random field of index 0 < [alpha] > 2 is derived. These random fields are of special interest in pattern analysis, in particular, in pattern synthesis. This paper considers the ease when the underlying graph that the random field is defined on is linear....</[alpha]>

Using a factorization of a standard Gaussian matrix, we show that a sequence of random variables, the finite sections of which are orthogonally invariant in distribution, must be a scale mixture of independent standard Gaussian variables.

If (Xk)[infinity]k = 1 is a sequence of independent random variables with probabilities of atoms bounded away from one and E is a Borel linear subspace of [infinity], then the event {(Xk)[infinity]k = 1 [set membership, variant] E} is a.s. equivalent to the event {(Xk)nk = 1 [set membership,...

Lower variance bounds are derived for functions of a random vector X, thus extending previous results. Moreover, the w-function associated X is shown to characterize its distribution, and a special application shows the multivariate central limit theorem.

A large amount of work has been carried out on finding joint distributions of X and Y with given margins which maximise the expected value of various returns c(X, Y). This paper connects the solution of such problems to a special class of relations, and obtains some specific and interesting...

A large deviation principle for U-statistics is presented. It relies on the large deviation for B-valued r.v. and on the spectral decomposition of the kernel of the U-statistic.

Suppose one observes a sample of size m from the mixture density [integral operator] p(xz) d[eta](z) and a sample of size n from the distribution [eta]. The kernel p(xz) is known. We show existence of the maximum likelihood estimator for [eta], characterize its support, and prove consistency as...

Our aim in this work is to give a global test of hypothesis concerning the smoothing spline estimate of a regression function. For this, we prove a central limit theorem for integrated squares of such estimates. That leads to a test whose confidence sets are either continuous or discrete...