Asymptotic inequalities are obtained for the level attained by any test statistic in a given hypothesis testing problem. The bounds so obtained are themselves random. The inequalities subsume previous results by Bahadur and others about the asymptotic behavior of attained levels. Various...

Let z(t) [set membership, variant] Rn be a generalized Poisson process with parameter [lambda] and let A: Rn -- Rn be a linear operator. The conditions of existence and limiting properties as [lambda] -- [infinity] or as [lambda] -- 0 of the stationary distribution of the process x(t) [set...

In this note a functional central limit theorem for [varrho]-mixing sequences of I. A. Ibragimov (Theory Probab. Appl. 20 (1975), 135-141) is generalized to nonstationary sequences (Xn)n [set membership, variant] , satisfying some assumptions on the variances and the moment condition E Xn2 + b =...

Presented here are results on almost sure convergence of estimators of regression functions subject to certain moment restrictions. Two somewhat different notions of almost sure convergence are studied: unconditional and conditional given a training sample. The estimators are local means derived...

Limit theorems are established for the reverse process of a critical multitype Galton-Watson process without variances. These results are an extension of those of Nakagawa 5 in the case with finite variances.

If X is a point random field on d then convergence in distribution of the renormalization C[lambda]X[lambda] - [alpha][lambda] as [lambda] -- [infinity] to generalized random fields is examined, where C[lambda] 0, [alpha][lambda] are real numbers for [lambda] 0, and X[lambda](f) =...

The rate of convergence of the least squares estimator in a non-linear regression model with errors forming either a [phi]-mixing or strong mixing process is obtained. Strong consistency of the least squares estimator is obtained as a corollary.

A general form for regular variation in IR2 is introduced and applied to domains of attraction of stable distribution in IR2 where the components have different indices. The situation in IRd with d > 2 is more complicated but not essentially different. For simplicity this paper is limited to IR2.

A theorem in [1] shows that the smallest eigenvalue of a class of large dimensional sample covariance matrices stays almost surely bounded away from zero. The theorem assumes a certain restriction on the class of matrices. With slight modifications of the proof in op cit, it is shown here that...

New integral and differential formulas for zonal polynomials are proved. As illustrations, zonal polynomials corresponding to partitions of two parts are computed. A method is presented, based on a certain partial differential operator, for expressing an orthogonally invariant polynomial as a...