Kendall Rank Correlation Let (X1, Y1), · · · , (Xn, Yn) be a bivariate random sample of size n. The Pearson correlation coefficient provides an optimal measure of the degree of association between the X’s and the Y ’s when the sample is drawn from a bivariate normal distribution. The Pearson correlation coefficient is reasonably robust for many other distributions as well. The Kendall correlati...

This paper describes the use of a microsphere sensor technology that allows simple fabrication of vapor sensor arrays with reproducible response patterns. Microsphere sensor fabrication protocols are uncomplicated and yield billions of highly reproducible sensors. Microsphere sensor arrays combined with a generalized Whitney-Mann-Wilcoxen (GWMW) classifier were used to discriminate between the ...

In this paper, we propose two regularization approaches for the Boltz-mann collision operator. The constructed operators preserve the mass, momentum and energy; their equilibrium states are Maxwellians and they satisfy the H theorem. In the rst approach, the regularization consists in allowing microscopic collisions which do not exactly preserve energy and momentum. However, the limit of the mo...

In a mathematical approach to hypothesis tests, we start with a clearly defined set of hypotheses and choose the test with the best properties for those hypotheses. In practice, we often start with less precise hypotheses. For example, often a researcher wants to know which of two groups generally has the larger responses, and either a t-test or a Wilcoxon-Mann-Whitney (WMW) test could be accep...