An L1 type inequality is proved between likelihood ratios and approximations to them gotten by conditioning on a finite number of random variables.

It is shown, with the use of a concentration inequality of LeCam, that associated with an infinitely divisible random variable with values in a separable Banach space there is a Lévy-Khintchine formula. A partial converse of this fact is also proved. Relations between the continuity of the...

A real-valued adapted sequence of random variables is an amart if and only if it can be written as a sum of a martingale and a sequence dominated in absolute value by a Doob potential, i.e., a positive supermartingale that converges to 0 in L1. The same holds for vector-valued uniform amarts...

Jensen's inequality f(EX) = Ef(X) for the expectation of a convex function of a random variable is extended to a generalized class of convex functions f whose domain and range are subsets of (possibly) infinite-dimensional linear topological spaces. Convexity of f is defined with respect to...

Let Sp-p have a Wishart distribution with unknown matrix [Sigma] and k degrees of freedom. For a matrix T(S) and a scalar h(S), an identity is obtained for E[summation operator]tr[h(S)T[summation operator]-1]. Two applications are given. The first provides product moments and related formulae...

A lower (upper) bound is given for the distribution of each dj, j = k + 1, ..., p (j = 1, ..., s), the jth latent root of AB-1, where A and B are independent noncentral and central Wishart matrices having Wp(q, [Sigma]; [Omega]) with rank ([Omega]) = K = p - s and Wp(n, [Sigma]), respectively....

A general method for determining the exact null density and distribution of U(p), a constant times Hotelling's generalized statistic, for integral values of m ( = (n1 - p - 1)/2) is provided by inversion of Laplace transforms. The density of U(p) has been given explicitly for p = 3 and 4, and...

In this article, we have considered the problem of testing equality of several growth curves under Behrens-Fisher situation. In this context, the robustness of the existing test criteria have been studied. Also, some exact test procedures have been considered and the exact and asymptotic...

This paper surveys the problem of estimating a linear relationship between variables which are observed with error. These are either fixed variables (functional relationship) or random variables (structural relationship). After considering various conditions for identifiability, estimation...

The following is an expository paper, containing few and sometimes incomplete proofs, on continuous tensor products of Hilbert spaces and of group representations, and on the irreducibility of the latter; the principal results in the last direction are due to Verchik, Gelfand, and Graiev. The...