Page 1 NSF-CBMS Regional Conference Series in Probability and Statistics Volume 2
EMPIRICAL PROCESSES: THEORY AND APPLICATIONS David Pollard Yale University …

A class of projection-based depth functions is introduced and studied. These projection-
based depth functions possess desirable properties of statistical depth functions and their …

A celebrated result of Black (1948a) demonstrates the existence of a simple-majority winner
when preferences are single-peaked. The social choice follows the preferences of the …

For a general definition of depth in data analysis a differential-like calculus is constructed in
which the location case (the framework of Tukey's median) plays a fundamental role similar …

A review is given of recent applications of empirical process theory and methods to statistics
with emphasis on empirical processes indexed by sets and functions. After a brief survey of …

We derive the asymptotic distribution of the maximal depth regression estimator recently
proposed in Rousseeuw and Hubert. The estimator is obtained by maximizing a projection …

Tukey's median is among one of the earliest known high breakdown point multivariate
location statistics. Aside from its breakdown point, though, little else appears to be known …

The asymptotic distribution of the Tukey median has recently been obtained by Nolan in a
bivariate setting and by Bai and He in the general multivariate case. To establish their …

The sensitivity of halfspace depth values and contours to perturbations of the underlying
distribution is investigated. The influence function of the halfspace depth of any point x∈ R p …

Data depth is a statistical method whose primary aim is to order data of a reference space
according to centrality. This is particularly appealing for directional data because no …