Statistical depth functions are being used increasingly in nonparametric multivariate data analysis. In a broad treatment of depth-based methods, Liu, Parelius, and Singh ("Multivariate analysis by date depth: Descriptive statistics, graphics and inference (with discussion)," 1999) include...

This paper develops a large deviation theorem for families of sample means of U-statistic structure (i.e., U-processes). These results extend the work of Sethuraman (1964) and Wu (1994) on large deviation theory for families of ordinary sample means and the classical empirical process. Along the...

The classical univariate sign and signed rank tests for location have been extended over the years to the multivariate setting, including recent robust rotation invariant "spatial" versions. Here we introduce a broad class of rotation invariant multivariate spatial generalized rank type test...

Given a multivariate probability distribution F, a corresponding depth function orders points according to their "centrality" in the distribution F. One useful role of depth functions is to generate two-dimensional curves for convenient and practical description of particular features of a...

Nonparametric notions of multivariate "scatter measure" and "more scattered," based on statistical depth functions, are investigated. In particular, notions of "more scattered" based on the "halfspace" depth function are shown to generalize versions introduced by P. J. Bickel and E. L. Lehmann...

Partial sums and sample means of r-dimensionally indexed arrays of independent random variables have been studied by Dunford (1951), Zygmund (1951), Kuelbs (1968), Wichura (1969), Smythe (1973), Gut (1978, 1992), Etemadi (1981), Klesov (1981, 1983), and Su and Taylor (1992), whose results cover...

Multivariate statistical analysis relies heavily on moment assumptions of second order and higher. With increasing interest in heavy-tailed distributions, however, it is desirable to describe dispersion, skewness, and kurtosis under merely first order moment assumptions. Here, the univariate...