Let X1, ..., Xn be i.i.d. S-valued random variables and let g be a real-valued function on S. We give an explicit representation of the conditional distribution of the empirical point process based on X1, ..., Xn given the (k + 1)th smallest order statistic of the r.v.'s g(X1), ..., g(Xn). The...

We show that the bootstrap approximation to the distribution of the Studentized trimmed mean performs better than the normal approximation, in that it is in error by terms of smaller order than n-1/2, where n denotes sample size. No assumptions are made about symmetry and only mild smoothness...

Let the vector X = [X1, ..., Xp]t have a multivariate normal distribution with unknown population mean vector [mu] and variance-covariance matrix [summation operator]. This paper develops minimally informative priors (in the sense of Bernardo) for use when the parameter of interest is either the...

For the multivariate normal mean vector testing problem, it is shown that in the light of power comparison, the restricted likelihood ratio test (LRT) is uniformly more powerful than the blobal version for the entire restricted parameter space in many cases.

In this article, we consider the problem of estimating a p-variate (p = 3) normal mean vector in a decision-theoretic setup. Using a simple property of the noncentral chi-square distribution, we have produced a sequence of smooth estimators dominating the James-Stein estimator and each improved...

In the normal two-sample problem, an invariant test for the hypothesis of the equality of the population covariance matrices, H:[Sigma]1 = [Sigma]2 vs A:[Sigma]1 [not equal to] [Sigma]2, has a power function which depends only on the eigenvalues of [Sigma]1[Sigma]2-1. An orthogonally invariant...

A function f([pi]) on the set of permutations of {1, 2, ..., n} is called arrangement increasing (AI) if it increases each time we transpose a pair of coordinates in descending order, i < j and [pi]i > [pi]j, putting them in ascending order. We define and develop a partial ordering =AI on densities of rank...</j>

The kernel estimator of a multivariate probability density function is studied. An asymptotic upper bound for the expected L1 error of the estimator is derived. An asymptotic lower bound result and a formula for the exact asymptotic error are also given. The goodness of the smoothing parameter...

In this paper a Bayesian alternative to Kriging is developed. The latter is an important tool in geostatistics. But aspects of environmetrics make it less suitable as a tool for interpolating spatial random fields which are observed successively over time. The theory presented here permits...

The multivariate regression of a p - 1 vector Y of random variables on a q - 1 vector X of explanatory variables is considered. It is assumed that linear transformations of the components of Y can be the basis for useful interpretation whereas the components of X have strong individual identity....