Hilbert spaces are characterized through the validity of the strong law of large numbers. Other characterizations of Hilbert spaces are also given at the same time in this note.

Estimators of the parameters of the functional multivariate linear errors-in-variables model are obtained by the application of generalized least squares to the sample matrix of mean squares and products. The generalized least squares estimators are shown to be consistent and asymptotically...

Suppose that X1, X2,..., Xn are independently distributed according to certain distributions. Does the distribution of the maximum of {X1, X2,..., Xn} uniquely determine their distributions? In the univariate case, a general theorem covering the case of Cauchy random variables is given here....

This paper deals with a quite general nonparametric statistical curve estimation setting. Special cases include estimation or probability density functions, regression functions, and hazard functions. The class of "fractional delta sequence estimators" is defined and treated here. This class...

In this paper, the authors proposed model selection methods for determination of the number of signals in presence of noise with arbitrary covariance matrix. This problem is related to finding the multiplicity of the smallest eigenvalue of [Sigma]2[Sigma]1-1, where [Sigma]2 = [Gamma] +...

Let X = {Xij:i, J = 1, 2,...} be an infinite dimensional random matrix, Tp be a p - p nonnegative definite random matrix independent of X, for p = 1, 2,.... Suppose (1/p) tr Tpk -- Hk a.s. as p -- [infinity] for k = 1, 2,..., and [Sigma]H2k-1/2k < [infinity]. Then the spectral distribution of Ap = (1/n) XpXp'Tp, where Xp = [Xij:i = 1,...,p; J = 1,...,n] tends to a nonrandom limit distribution as p --> [infinity], n -- [infinity], but p/n -- y 0,...</[infinity].>

We obtain strong approximation results for the empirical Q-Q process. Moreover, some Glivenko-Cantelli-type results are also obtained. These results are applicable to construct confidence bands for Q-Q plots.

An explicit formula is obtained for the nonlinear predicion of Y(t) = Xn(t), where X(t) is an N-ple Gaussian Markov process.

It is a well known part of statistical knowledge that first order asymptotically efficient procedures can be misleading for moderate sample sizes. Usually this is demonstrated for some popular special cases including numerical comparisons. Typically the situation is worse if nuisance parameters...

It is proved that a nondegenerate diffusion process in the closed half space , where d >= 2, with Wentzell's boundary conditions does not hit any specified point on the boundary.