Search results for "Statistique mathématique"
showing 3 items of 3 documents
Historical and Technical Notes on Aqueducts from Prehistoric to Medieval Times
2013
The aim of this paper is to present the evolution of aqueduct technologies through the millennia, from prehistoric to medieval times. These hydraulic works were used by several civilizations to collect water from springs and to transport it to settlements, sanctuaries and other targets. Several civilizations, in China and the Americas, developed water transport systems independently, and brought these to high levels of sophistication. For the Mediterranean civilizations, one of the salient characteristics of cultural development, since the Minoan Era (ca. 3200-1100 BC), is the architectural and hydraulic function of aqueducts used for the water supply in palaces and other settlements. The M…
Optimal signed-rank tests based on hyperplanes
2005
Abstract For analysing k -variate data sets, Randles (J. Amer. Statist. Assoc. 84 (1989) 1045) considered hyperplanes going through k - 1 data points and the origin. He then introduced an empirical angular distance between two k -variate data vectors based on the number of hyperplanes (the so-called interdirections ) that separate these two points, and proposed a multivariate sign test based on those interdirections. In this paper, we present an analogous concept (namely, lift-interdirections ) to measure the regular distances between data points. The empirical distance between two k -variate data vectors is again determined by the number of hyperplanes that separate these two points; in th…
Affine-invariant rank tests for multivariate independence in independent component models
2016
We consider the problem of testing for multivariate independence in independent component (IC) models. Under a symmetry assumption, we develop parametric and nonparametric (signed-rank) tests. Unlike in independent component analysis (ICA), we allow for the singular cases involving more than one Gaussian independent component. The proposed rank tests are based on componentwise signed ranks, à la Puri and Sen. Unlike the Puri and Sen tests, however, our tests (i) are affine-invariant and (ii) are, for adequately chosen scores, locally and asymptotically optimal (in the Le Cam sense) at prespecified densities. Asymptotic local powers and asymptotic relative efficiencies with respect to Wilks’…