It is shown in this note that the one-term Edgeworth expansion for the standardized sample mean of n independent lattice random vectors when perturbed by a random variable (1/[radical sign]n) U is the same as in the strongly non-lattice case, where U is a bounded random variable depending only...

The r-quick limit points of normalized sample paths and empirical distribution functions of mixing processes are characterized. An r-quick version of Bahadur-Kiefer-type representation for sample quantiles is established, which yields the r-quick limit points of quantile processes. These results...

A set of n points sampled from a common distribution F, is partitioned into k = 2 groups that maximize the between group sum of squares. The asymptotic normality of the vector of probabilities of lying in each group and the vector of group means is known under the condition that a particular...

Consistent estimators for the reciprocal of the density at a quantile point, which is the derivative of the quantile function, are considered. Rates of convergence of these estimators, depending on the smoothness properties of the density, are obtained. Two different, but natural, estimators of...

Consistent estimators for the reciprocal of the density at a quantile point are considered. Optimal rates of convergence of these estimators, depending on the smoothness properties of the density, are obtained. An symptotically efficient estimator sequence, in the mean square error sense, is...

Edgeworth expansions which are local in one coordinate and global in the rest of the coordinates are obtained for sums of independent but not identically distributed random vectors. Expansions for conditional probabilities are deduced from these. Both lattice and continuous conditioning...

Let G be a distribution function on 1 such that the (k + 1)th marginal is lattice. Let Zn denote the sampe mean of n independent observations from G. For s [greater-or-equal, slanted] 3, the s-term Edgeworth expansions are obtained for a wide class of statistics which are smooth functions of Zn....

Edgeworth expansions for sums of independent but not identically distributed multivariate random vectors are established. The results are applied to get valid Edgeworth expansions for estimates of regression parameters in linear errors-in-variable models. The expansions for studentized versions...

The asymptotic theory of k-mean clustering is extended to stationary mixing processes, both [sigma]-mixing and strong-mixing. In addition, a consistency result is obtained for non-identically distributed independent observations.