It is shown that 2-parameter strong martingales in the sense of Walsh can be transformed into 1-parameter martingales by the "embedding of tactics" and can be characterized by this property.

Consider an array of random variables (Xi,j), 1 = i,j [infinity], such that permutations of rows or of columns do not alter the distribution of the array. We show that such an array may be represented as functions f([alpha], [xi]i, [eta]j, [lambda]i,j) of underlying i.i.d, random variables....

Let = (1, 2, ..., n)' be the least-squares estimator of [theta] = ([theta]1, [theta]2, ..., [theta]n)' by the realization of the process y(t) = [Sigma]k = 1n [theta]kfk(t) + [xi](t) on the interval T = [a, b] with f = (f1, f2, ..., fn)' belonging to a certain set X. The process satisfies...

The almost sure convergence of the kernel-type density estimate is proved for a strictly stationary ergodic sample.

Sheppard's corrections for grouping can, in the case of an underlying normal distribution, be interpreted as a first step to the solution of the maximum likelihood equations which incorporate the grouping problem. This result of Lindley (for the univariate) and Haitovsky (for the bivariate) is...

In this paper a large class of multivariate densities and frequency functions, including the multivariate Poisson distribution and the compound multivariate Poisson distribution, are shown to have the decreasing in transposition property introduced by [4], Ann. Statist. 5, 722-733). Sample...

For the p-variate Poisson mean, under the sum of weighted squared error losses, weights being reciprocals of variances, a class of proper Bayes minimax estimates dominating the usual estimate, namely the sample mean is produced. An example is given to illustrate this. The interrelation of our...

Let Y be an absolutely continuous random variable and W a nonnegative variable independent of Y. It is to be expected that when W is close to 1 in some sense, the distribution of the scale mixture YW will be close to Y. This notion has been investigated by a number of workers, who have provided...

Sharpe investigated the structure of full operator-stable measures [mu] on a vector group V and obtained decompositions, [mu] = [mu]1 * [mu]2 and V = V1 [circle plus operator] V2, in terms of the Gaussian component [mu]1 and the Poisson component [mu]2. The subspaces V1 and V2 are here...