Let [mu] be a positive finite Borel measure on the real line R. For t = 0 let et · E1 and E2 denote, respectively, the linear spans in L2(R, [mu]) of {eisx, s t} and {eisx, s < 0}. Let [theta]: R --> C such that theta; = 1, denote by [alpha]t([theta], [mu]) the angle between [theta] · et · E1 and E2. The...</0}.>

An approximate maximum likelihood procedure is proposed for the estimation of parameters in possibly nonminimum phase (noninvertible) moving average processes driven by independent and identically distributed non-Gaussian noise. Under appropriate conditions, parameter estimates that are...

A system of particles of k types with immigration in Rd is considered. Each particle, according to its type, independently migrates following a symmetric stable process, lives an exponential amount of time and produces particles of all the types. The asymptotic behavior of the vector measure...

Consider a stationary time series (Xt, Yt), t = 0, ±1, ... with Xt being d-valued and Yt real-valued. Let [psi](·) denote a monotone function and let [theta](·) denote the robust conditional location functional so that E[[psi](Y0 - [theta](X0))X0] = 0. Given a finite realization (X1,...

In this paper, it is shown that two random matrices have a joint matrix variate normal distribution if, conditioning each one on the other, the resulting distributions satisfy certain conditions. A general result involving more than two matrices is also proved.

Let S: p - p have a nonsingular Wishart distribution with unknown matrix [Sigma] and n degrees of freedom, n = p. For estimating [Sigma], a family of minimax estimators, with respect to the entropy loss, is presented. These estimators are of the form (S) = R[Phi](L) Rt, where R is orthogonal, L...

Let [mu] be a positive finite Borel measure on the real line R. For t = 0 let et · E1 and E2 denote, respectively, the linear spans in L2(R, [mu]) of {eisx, s t} and {eisx, s < 0}. Let [theta]: R --> C such that [short parallel][theta][short parallel] = 1, denote by [alpha]t([theta], [mu]) the angle between [theta]...</0}.>

A linear model with random effects, [mu]i, and random error variances, [sigma]i, is considered. The linear Bayes estimator or the best linear unbiased predictor (BLUP) of [mu]i is first obtained, and then the unknown parameters in the model are estimated to arrive at the empirical linear Bayes...

Edgeworth expansions for sums of independent but not identically distributed multivariate random vectors are established. The results are applied to get valid Edgeworth expansions for estimates of regression parameters in linear errors-in-variable models. The expansions for studentized versions...

Based on a martingale analogue of Kolmogorov's law of the iterated logarithm, we obtained a log log law for unstable ARMA processes, that is, , a.s., and (, a.s., where b is an arbitrary constant, , {X(k)} is an unstable ARMA process [phi](B) X(n) = C(B) [var epsilon](n), d is the largest...