Given the linear model b = Ax - [var epsilon], where x and [var epsilon] are Gauss distributed with covariance operators Rx and R[var epsilon], R[var epsilon] positive definite; then b(x) = RxA'(ARxA' + R[var epsilon])-1b is the expectation of the conditional distribution of x relative to b. This...

Let S1 and S2 be two independent p - p Wishart matrices with S1 ~ Wp([Sigma]1, n1) and S2 ~ Wp([Sigma]2, n2). We wish to estimate [zeta] = [Sigma]2[Sigma]1-1 under the loss function L1 = tr([zeta] - [zeta])' [Sigma]2-1([zeta] - [zeta]) [Sigma]1/tr [zeta]. By extending the techniques of Berger,...

We present strong laws of large numbers, central limit theorems and laws of the iterated logarithm for the growth of some random walks on free groups and semigroups which generalize isotropic random walks. Our method to derive these results is based on corresponding limit theorems on polynomial...

In this paper we will set up the Hida theory of generalized Wiener functionals using *(d), the space of tempered distributions on d, and apply the theory to multiparameter stochastic integration. With the partial ordering on +d: (s1, ..., sd) < (t1, ..., td) if si < ti, 1 <= i <= d, the Wiener process W((t1 ..., td), x) = <x, 1[0,t1)x ... x[0,td)>, [xi] [epsilon] I*(Td) is a generalization of a...</(t1,>

For any distribution belonging to the Kagan class a general formula expressing its characteristic function in a neighbourhood of the origin in terms of the marginal characteristic functions is obtained. Also some applications are given.

The speed of a.s. uniform convergence of nonparametric curve estimators for mn-decomposable processes is studied. Such processes include, e.g., linear and bilinear processes. A simple and straghtforward method is used relating this kind of problem to compound empirical processes (i.e., empirical...

We investigate nonparametric curve estimation (including density, distribution, hazard, conditional density, and regression functions estimation) by kernel methods when the observed data satisfy a strong mixing condition. In a first attempt we show asymptotic equivalence of average square...

Let {(Xi, Yi); I = 1,2,...} be a sequence of i.i.d. r.v.'s and denote by m(y x0), -[infinity] y [infinity], the conditional distribution function of Y given X = x0, -[infinity] x0 [infinity]. In this paper we propose and discuss certain smooth variants (based both on single as well as double...

We discuss a maximum likelihood procedure for estimating parameters in possibly noncausal autoregressive processes driven by i.i.d. non-Gaussian noise. Under appropriate conditions, estimates of the parameters that are solutions to the likelihood equations exist and are asymptotically normal....

The problem of finding classes of estimators which improve upon the usual (e.g., ML, LS) estimator of the parameter matrix in the GMANOVA model under (matrix) quadratic loss is considered. Classes of improved estimators are obtained via combining integration-by-parts methods for normal and...