The asymptotic properties of a multivariate location estimator are obtained in this paper. The estimator examined is based on the notion of half-space depth, where the depth of a point is the minimum probability content of all half spaces containing the point. The location estimator of interest...

A location-adaptive hybrid of the fixed-bandwidth kernel density estimate and the nearest-neighbor density estimate is introduced in this paper. It is constructed via a simple adhoc truncation and smoothing of nearest-neighbor distance. Simulations show that the hybrid outperforms its parent...

One version of multivariate trimming is the operation that intersects all halfspaces with probability content 1-[alpha] or greater. The result is a [alpha]-trimmed convex set, and this set is stochastic when the empirical distribution of a sample determines the probability content of the...

The excess-mass ellipsoid is the ellipsoid that maximizes the difference between its probability content and a constant multiple of its volume, over all ellipsoids. When an empirical distribution determines the probability content, the sample excess-mass ellipsoid is a random set that can be...

A model is developed for multivariate distributions which have nearly the same marginals, up to shift and scale. This model, based on "interpolation" of characteristic functions, gives a new notion of "correlation". It allows straightforward nonparametric estimation of the common marginal...

Kernel density estimators are used for the estimation of integrals of various squared derivatives of a probability density. Rates of convergence in mean squared error are calculated, which show that appropriate values of the smoothing parameter are much smaller than those for ordinary density...

Long-range-dependent time series are endemic in the statistical analysis of Internet traffic. The Hurst parameter provides a good summary of important self-similar scaling properties. We compare a number of different Hurst parameter estimation methods and some important variations. This is done...