Let (X1,X2,...,Xn) and (Y1,Y2,...,Yn) be gamma random vectors with common shape parameter [alpha] (0<[alpha][less-than-or-equals, slant]1) and scale parameters ([lambda]1,[lambda]2,...,[lambda]n), ([mu]1,[mu]2,...,[mu]n), respectively. Let X()=(X(1),X(2),...,X(n)), Y()=(Y(1),Y(2),...,Y(n)) be the order statistics of (X1,X2,...,Xn) and (Y1,Y2,...,Yn). Then ([lambda]1,[lambda]2,...,[lambda]n) majorizes ([mu]1,[mu]2,...,[mu]n) implies that X() is stochastically larger than Y(). However if the common shape parameter [alpha]>1, we can only compare the the first- and last-order statistics. Some earlier results on stochastically comparing proportional hazard functions are shown to be special cases of our results.

The limit behavior of the conditional probability of error of linear and quadratic discriminant analyses is studied under wide assumptions on the class conditional distributions. Results obtained may help to explain analytically the behavior in applications of linear and quadratic discrimination...

This paper gives results for the population value of a measure of the goodness-of-fit of a general multivariate normal distribution to the simpler hypothesis of independent normal variables. The measure was introduced by Rudas, Clogg and Lindsay in 1994, who gave the value for the bivariate...

For multivariate regressors, integrating the Nadaraya-Watson regression smoother produces estimators of the lower-dimensional marginal components that are asymptotically normally distributed, at the optimal rate of convergence. Some heuristics, based on consistency of the pilot estimator,...

In this paper it is studied how observations in the training sample affect the misclassification probability of a quadratic discriminant rule. An approach based on partial influence functions is followed. It allows to quantify the effect of observations in the training sample on the performance...

We show that the problem of searching for v-structures in a directed acyclic graph can be decomposed into searches in its decomposed subgraphs. This result simplifies the search for v-structures and the recovery of local causal relationships.

For two-way ordered categorical data, correspondence analysis and the RC association model (the row-column-effect association model) with order-restricted scores have been proposed mainly for descriptive purposes. In this paper, tests for independence in two-way ordered contingency tables based...

In this paper, we use a combination of VDR theory and patchwork method to derive an efficient algorithm for generating uniform random points on a unit d-sphere. We first propose an algorithm to generate random vector with uniform distribution on a unit 2-sphere on the plane. Then we use VDR...

We show that if a process can be obtained by filtering an autoregressive process, then the asymptotic distribution of sample autocovariances of the former is the same as the asymptotic distribution of linear combinations of sample autocovariances of the latter. This result is used to show that...

We analyze in a regression setting the link between a scalar response and a functional predictor by means of a Functional Generalized Linear Model. We first give a theoretical framework and then discuss identifiability of the model. The functional coefficient of the model is estimated via...