In this paper, several distributional properties and characterization theorems of the generalized multivariate Pareto distributions are studied. It is found that the multivariate Pareto distributions have many mixture properties. They are mixed either by geometric, Weibull, or exponential...

In computer science, an ontology is any formally structured vocabulary covering a conceptual domain. Gene Ontology (GO) is a structured collection of terms defining biological processes, cellular components, or molecular functions for the purpose of characterizing gene products and functions....

In this work, we assess the suitability of cluster analysis for the gene grouping problem confronted with microarray data. Gene clustering is the exercise of grouping genes based on attributes, which are generally the expression levels over a number of conditions or subpopulations. The hope is...

In this paper we investigate the weighted bootstrap for U-statistics and its properties. Under very general choices of random weights and certain regularity conditions, we show that the weighted bootstrap method with U-statistics provides second-order accurate approximations to the distribution...

For the purpose of testing the spherical uniformity based on i.i.d. directional data (unit vectors) zi, i=1,...,n, Anderson and Stephens (Biometrika 59 (1972) 613-621) proposed testing procedures based on the statistics Smax=maxu S(u) and Smin=minu S(u), where u is a unit vector and nS(u) is the...

We provide lattice decompositions for multivariate distributions. The lattice decompositions reveal the structural relationship between the Lancaster/Bahadur model and the model of Streitberg (Ann. Statist. 18 (1990) 1878). For multivariate categorical data, the decompositions allows modeling...

The fundamental best-possible bounds inequality for bivariate distribution functions with given margins is the Frechet-Hoeffding inequality: If H denotes the joint distribution function of random variables X and Y whose margins are F and G, respectively, then...

This paper is concerned with a change-point problem in random fields. Tests for detecting a change-structure in a two-way table are constructed. Solutions to this problem require calculations of multiple integrals, but the calculations become difficult as the table gets large. To overcome this...

In this paper we propose a new test for the multivariate two-sample problem. The test statistic is the difference of the sum of all the Euclidean interpoint distances between the random variables from the two different samples and one-half of the two corresponding sums of distances of the...

Much work in discriminant analysis and statistical pattern recognition has been performed in the former Soviet Union. However, most results derived by former Soviet Union researchers are unknown to statisticians and statistical pattern recognition researchers in the West. We attempt to give a...