Bayesian estimation of the cell probabilities for the multinomial distribution (under a symmetric Dirichlet prior) leads to the use of a flattening constant [alpha] to smooth the raw cell proportions. The unsmoothed estimator corresponds to [alpha] = 0. The risk functions (under quadratic loss)...

This paper deals with multivariate stable distributions. [6], 444-462]. We present counter-examples and correct proofs of some of the statements of Press. The properties of multivariate stable distributions, connected with the spectral measure [Gamma], present in the expression of the...

One result of Smirnov's important paper [Uspehi Mat. Nauk. 10, 179-206, (in Russian)] yields exponential bounds for the large deviations of his one-sided Smirnov statistic and the two-sided Kolmogorov statistic. In the present paper exponential bounds are given for the large deviations of a wide...

In our preceding paper [1], we have studied the fundamental properties of the direct limits of measure spaces. The present article is devoted to the study of the integration of direct limits of direct systems of real measurable functions, and in particular, of direct limits of systems of real...

Let X1(1 - 1), X2(1 - p2), and X3(1 - p3) be three sets of random variables distributed jointly as a normal distribution. Let [varrho]1.23 and [varrho]1.2 be the multiple correlation coefficients between X1 and (X2, X3) and between X1 and X2, respectively. Invariant tests for the following four...

For profile analysis of independent samples from several multivariate populations, a nonparametric analog of the hypothesis of parallelism of population profiles is formulated. A class of asymptotically distribution-free statistics is offered to test this hypothesis. These are based on...

We derive various results for the uniform distribution on a Stiefel manifold and propose a test of uniformity.

Let p be an infinitely divisible n-variate probability having [mu] for Poisson measure. We give here some sufficient conditions for p to belong to the class of n-variate probabilities having only infinitely divisible [alpha]-factors. These results are interesting since they are concerned with...

The characterization problem of a homogeneous Markov chain (with either finitely many or a countable number of states) is considered for the class of the variables satisfying the asymptotic independence. An allied result when some state distribution is given beforehand at some step is also...

We extend the Lévy inversion formula for the recovery of a bounded measure over from its Fourier-Stieltjes transform to bounded complex-valued, orthogonally scattered Hilbert space-valued, and spectral projection operator-valued measures over any first countable locally compact Abelian group....