We find necessary and sufficient conditions for the convergence of (matrix) normed and centered k-variate binomial vectors to a full k-variate normal law. The norming matrices are also characterized. A converse to the univariate Laplace-De Moivre Theorem is obtained.

It is shown that when the random vector X in Rn has a mean and when the conditional expectation E(u'Xv'X) = 0 for all vectors u, v [set membership, variant] Rn which satisfy u'v = 0, then the distribution of X is orthogonally invariant. A version of this characterization is also established when...

The estimated weighted empirical quantile process is introduced, and under mild regularity conditions is shown to converge weakly in L2(0, 1) to a Gaussian process. This leads to an elementary approach to the derivation of the asymptotic null distribution of Cramér-von Mises type statistics for...

This article is concerned with hierarchical prior distributions and the effect of replacing the distribution of a component in the hierarchy with a diffuse distribution where all nondiffuse distributions are multivariate normal. Let f denote the posterior density function and g = gm, the...

Let be an estimator obtained by integrating a kernel type density estimator based on a random sample of size n from a (smooth) distribution function F. Sufficient conditions are given for the central limit theorem to hold for the target statistic where {Un} is a sequence of U-statistics.

Nonsingular limit distributions are determined for sequences of affine transformations of random vectors whose distributions are multivariate binomial. Each of these limit distributions is that of an affine transformation of a random vector having a multivariate normal distribution or a...

Certain path properties of a symmetric [alpha]-stable process X(t) = [integral operator]Sh(t, s) dM(s), t [set membership, variant] T, are studied in terms of the kernel h. The existence of an appropriate modification of the kernel h enables one to use results from stable measures on Banach...

In this paper we investigate various third-order asymptotic properties of maximum likelihood estimators for Gaussian ARMA processes by the third-order Edgeworth expansions of the sampling distributions. We define a third-order asymptotic efficiency by the highest probability concentration around...

We present a new method of computing C. R. Rao's MINQUE in variance component models (y = X[beta] + U1[xi]1 + ... + Up[xi]p), which requires only inversion and storage of ni - ni matrices, where ni is the number of columns in Ui. In many cases most of these matrices are of diagonal form. In...