Let Ui = (Xi, Yi), i = 1, 2,..., n, be a random sample from a bivariate normal distribution with mean [mu] = ([mu]x, [mu]y) and covariance matrix . Let Xi, i = n + 1,..., N represent additional independent observations on the X population. Consider the hypothesis testing problem H0 : [mu] = 0...

Let be a real separable Hilbert space; let X(t), t[epsilon][0, 1], be a separable, stochastically continuous, -valued stochastic process with independent increments. Then a decomposition of X(t) into a uniformly convergent sum of independent processes is found. In this decomposition one of the...

Subclasses L0 [superset or implies] L1 [superset or implies] ... [superset or implies] L[infinity] of the class L0 of self-decomposable probability measures on a Banach space are defined by means of certain stability conditions. Each of these classes is closed under translation, convolution and...

Let {Xn} be a strictly stationary [phi]-mixing process with [Sigma]j=1[infinity] [phi]1/2(j) [infinity]. It is shown in the paper that if X1 is uniformly distributed on the unit interval, then, for any t [set membership, variant] [0, 1], Fn-1(t) - t + Fn(t) - t = O(n-3/4(log log n)3/4) a.s. and...

This paper deals with asymptotic expansions for the non-null distributions of certain test statistics concerning a correlation matrix in a multivariate normal distribution. For this purpose an asymptotic expansion is given for the distribution of a function of the sample correlation matrix. As...

We consider two Gaussian measures P1 and P2 on (C(G), ) with zero expectations and covariance functions R1(x, y) and R2(x, y) respectively, where R[nu](x, y) is the Green's function of the Dirichlet problem for some uniformly strongly elliptic differential operator A([nu]) of order 2m, m = [d/2]...

This paper presents some generalizations of S. N. Bernstein's exponential bounds on probabilities of large deviations to the vector case. Inequalities for probabilities of large deviations of sums of independent random vectors are derived under a Cramér's type restriction on the rate of growth...

We consider L1 bounded martingales on a von Neumann algebra with respect to a given ascending sequence of von Neumann subalgebras as functionals on the C*-algebra which is the uniform closure of the union of those subalgebras. We define the singular martingales, prove the "Krickeberg...

Random variables X1 ,..., Xn are said to have a joint distribution with Weibull minimums after arbitrary scaling if mini(aiXi) has a one dimensional Weibull distribution for arbitrary constants ai 0, I = 1,..., n. Some properties of this class are demonstrated, and some examples are given which...

Let the process {Y(x,t) : t [epsilon] T} be observable for each x in some compact set X. Assume that Y(x, t) = [theta]0f0(x)(t) + ... + [theta]kfk(x)(t) + N(t) where fi are continuous functions from X into the reproducing kernel Hilbert space H of the mean zero random process N. The optimum...