LJKProbability & Statistics Seminar

On Thursday January 7 2016 at 14h00 in Salle 1  Tour IRMA

Seminary of Mr Luc PRONZATO (Université Nice Sophia Antipolis)

A measure of dispersion based on average exponentiated volumes, with application in experimental design

Summary

(joint work with Henry P. Wynn, LSE, and Anatoly A. Zhigljavsky, Cardiff University)
We consider a measure of dispersion in dimension d which is based on the mean exponentiated volume of kdimensional simplices formed by k+1 independent copies, with k less than or equal to d. The mean squared volume is related to the (dk)th coefficient of the characteristic polynomial of the covariance matrix and forms an extension of the notion of Wilk's generalised variance. We prove its concavity when raised at power 1/k, and some properties of dispersionmaximising distributions are derived, including a necessary and sufficient condition for optimality. The application of this measure of dispersion to the design of optimal experiments for parameter estimation is considered, with A and Doptimal design coinciding with the special cases obtained for k=1 and k=d respectively. Means of volumes raised to some power different from two, including negative values, will be considered too, with application to spacefilling design for computer experiments.
