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...

The kernel function in density estimation is uniquely determined up to a scale factor. In this paper, we advocate one particular rescaling of a kernel function, called the canonical kernel, because it is the only version which uncouples the problems of choice of kernel and choice of scale...