A general easily checkable Cochran theorem is obtained for a normal random operator Y. This result does not require that the covariance, [Sigma]Y, of Y is nonsingular or is of the usual form A [circle times operator] [Sigma] ; nor does it assume that the mean, [mu], of Y is equal to zero....

We consider the estimation of the multivariate probability density functions of stationary random processes from noisy observations. The asymptotic normality of kernel-type deconvolution estimators is established for various classes of mixing processes. Classes of noise characteristic functions...

When samples are taken from a (multivariate) normal distribution then under suitable conditions we characterize the greatest class of priors such that the posterior distribution is also (multivariate) normal. In this case exact formulas are given showing how the mean and covariance matrix of the...

We prove limit theorems of functional type for weighted U-statistics with varying kernel. In particular, we show that the Lévy-Prokhorov distance between these processes un and certain processes vn constructed from i.i.d. standard normal variables converges to zero. Limit results for un follow...

We derive a functional limit theorem for a sequence of bandwidth processes with multivariate time and show that the limit process is multivariate Gaussian. This theorem is then applied to show asymptotic efficiency of certain data-adaptive local bandwidth choices for kernel estimators of...

It is a well-known result (which can be traced back to Gauss) that the only translation family of probability densities on for which the arithmetic mean is a maximum likelihood estimate of the translation parameter originates from the normal density. We generalize this characterization of the...

We find a necessary and sufficient condition for joint asymptotic independence of componentwise processes of record times generated by a multivariate random sample.

Let x1, ..., xj, ..., xn be n independent realizations of a p-dimensional random variable X which has the elliptical t-distribution of the form g(x) = K([nu], p) [Sigma]-1/2 [([nu] - 2) + (x - [theta])' [Sigma]-1(x - [theta])]-([nu] + p)/2, where [theta] and [Sigma] denote the p - 1 location...

This paper makes an asymptotic comparison, up to the third order, between the locally most mean power unbiased (LMMPU) and Rao's tests in the multi-parameter case. The two tests are seen to have identical power up to second order. It is also seen that Rao's test, which is much simpler than the...

A classic result in probability theory states that two independent real-valued random variables having independent sum and difference are either constant or normally distributed with the same variance. In this article conditions are round on independent random variables X and Y taking values in...