It is well known that symmetric statistics based on a kernel with finite second moment have a limit law which can be described by a multiple Wiener-Ito integral. However, if the kernel has less than second moments, no weak limit law holds in general. In the present paper we show that by a...

Comparisons are made between the expected gain of a prophet (an observer with complete foresight) and the maximal expected gain of a gambler (using only non-anticipating stopping times) observing a sequence of independent, uniformly bounded random variables where a non-negative fixed cost is...

Problems associated with the parametric modelling of multivariate input output systems are addressed in this paper. A three stage estimation procedure is proposed, each stage being implemented by means of straighforward closed form multivariate least squares regressions. The statistical...

The usual confidence set for a multivariate mean vector can be improved upon by recentering the set at a Stein-type estimator: this fact is known to be true under many different distributional assumptions. Thus far, however, the case of unknown variance has not been dealt with analytically. In...

In this article it is shown that when the pdff(x) is non-increasing in xi, i = 1, 2, ..., k, the sphere of diameter d centred at the origin has largest probability content as compared to any other region of diameter at most d. As a consequence, it follows that a sphere of diameter d has largest...

The Robbins-Monto processes in a Hilbert space are considered in this work. A nonlinear mapping f is treated instead of the usual linearity assumption. A modified process with varying truncations is analyzed, and asymptotic properties are investigated. Convergence as well as necessary and...

Consider the linear model Y = X[beta] + [epsilon], where Y is the response variable of order (n-1), X is an (n-p) matrix of known constants, [beta] is a (p-1) unknown parameter, [epsilon] is an (n-1) error variable with E([epsilon]) = 0, and E([epsilon][epsilon]') = [sigma]2[Lambda], where...

A general procedure for constructing sequential confidence sets for a vector valued parameter, having a coverage probability at least 1-[alpha] and probability of covering a certain set of false values at most [beta], is developed. The limiting values of the error probabilities are found as the...

Let X1,...,Xn (n1, p1) be independently and identically distributed normal p-vectors with mean [mu] and covariance matrix ([mu]'[mu]/C2)I, where the coefficient of variation C is known. The authors have obtained the best equivariant estimator of [mu] under the loss function...

Consider the nonparametric regression model Yi(n) = g(xi(n)) + [var epsilon]i(n), i = 1, ..., n, where g is an unknown regression function and assumed to be bounded and real valued on A [subset of] Rp, xi(n)'s are known and fixed design points and [var epsilon]i(n)'s are assumed to be both...