Inhomogeneous linear estimation in the general mixed model with possible singular covariance matrix is considered. It is shown that this problem reduces to the homogeneous linear estimation in a simpler model. In consequence, some necessary and sufficient conditions for the admissibility are...

Generalizations of prophet inequalities for single sequences are obtained for optimal stopping of several parallel sequences of independent random variables. For example, if {Xi, j, 1 = i = n, 1 = j [infinity]} are independent non-negative random variables, then and this bound is best possible....

The validity of formal Edgeworth expansions for statistics which are functions of sample averages was established in [2], Ann. Statist.6 434-451) under a moment condition which is sometimes too severe. In this article this moment condition is relaxed. Two examples of [6 and 7], Ann. Probab.15...

[1], 641-643) have given a characterization of the Dirichlet distributions based on the properties of independence of various functions of the random variables (X1, X2, ..., Xk) having a joint continuous distribution over the k-dimensional simplex: 0 = x1 = [Sigma] xi = 1. In this paper we...

The identity map on the set of functions of bounded variation under the variation norm to the same set under supremum norm is of type 2.

We consider the asymptotic expansions for the distribution of the von Mises statistical functionals. By combining the methods of Reeds [6] and Callaert et al. [1], we obtain the Edgeworth expansion with remainder o(n-1/2) as n --> [infinity].

Let {Vn; n = 1} be a sequence of random elements in a separable normed linear space E, uniformly dominated by a random variable V. Let {Ank; K = 1, 2, ..., n; n = 1} be a triangular array of random variables. In this paper, conditions for the convergence of [Sigma]k=1n AnkVk to zero (in...

The central limit theory associated with universally optimal and bounded locally optimal clustering is presented. The derivation makes use of a Donsker-type theorem for the quantile process that is also proven. Procedures for assessing the numbers of groups represented in the data are also...

With (X1, X2) in a stable domain of attraction and (Y1, Y2) independent of (X1, X2), conditions are given for which (X1Y1, X2Y2) is in the same domain and for which the same norming constants are applicable. For the case with no normal component, an alternative criterion for stable attraction...

The asymptotic minimax theorem of LeCam and Hájek is refined by inclusion of terms of order n-1/2. This renders more precise informations about the local properties of superefficient estimator-sequences.