Estimation of variance components in linear model theory is presented as an application of estimation of the mean by introducing a dispersion-mean correspondence. Without any further computations, this yields most general representations of minimum variance-minimum bias-invariant quadratic...

The collision problems of two-parameter random walks are studied. That is, some criteria have been established in terms of the characteristic functions of two or more mutually independent random walks in order to determine if they meet infinitly often in certain restricted time sets.

The behavior of the posterior for a large observation is considered. Two basic situations are discussed; location vectors and natural parameters. Let X = (X1, X2, ..., Xn) be an observation from a multivariate exponential distribution with that natural parameter [Theta] = ([Theta]1, [Theta]2, ...,...

In 1974, Sen proved weak convergence of the empirical processes (in the J1-topology on Dp[0, 1]) for a stationary [phi]-mixing sequence of stochastic p([greater, double equals] 1)-vectors. In this note, we show that Sen's theorem on weak convergence of the multidimensional empirical process for...

In this paper it is shown that every nonnegative definite symmetric random matrix with independent diagonal elements and at least one nondegenerate nondiagonal element has a noninfinitely divisible distribution. Using this result it is established that every Wishart distribution Wp(k, [Sigma],...

Let [Sigma] be an n - n positive definite matrix with eigenvalues [lambda]1 = [lambda]2 = ... = [lambda]n 0 and let M = {x, y x [epsilon] Rn, y [epsilon] Rn, x [not equal to] 0, y [not equal to] 0, x'y = 0}. Then for x, y in M, we have that x'[Sigma]y/(x'[Sigma]xy'[Sigma]y)1/2 = ([lambda]1 -...

The asymptotic behavior, for large sample size, is given for the distribution of the canonical correlation coefficients. The result is used to examine the Bartlett-Lawley test that the residual population canonical correlation coefficients are zero. A marginal likelihood function for the...

For Gaussian vector fields {X(t) [set membership, variant] Rn:t [set membership, variant] Rd} we describe the covariance functions of all scaling limits Y(t) = lim[alpha][downwards arrow]0 B-1([alpha]) X([alpha]t) which can occur when B([alpha]) is a d - d matrix function with B([alpha]) -- 0....

Consistent, asymptotically efficient and asymptotically normal stepwise estimators are given for a subclass of the uniparametric and multiparametric exponential families. The estimators are derived by using the Robbins-Monro stochastic approximation procedure with certain families of random...