Data depth measures the centrality of a point with respect to a given distribution or data cloud. It provides a natural center-outward ordering of multivariate data points and yields a systematic nonparametric multivariate analysis scheme. In particular, the halfspace depth is shown to have many...

Using the <italic>DD</italic>-plot (depth vs. depth plot), we introduce a new nonparametric classification algorithm and call it <italic>DD</italic>-classifier. The algorithm is completely nonparametric, and it requires no prior knowledge of the underlying distributions or the form of the separating curve. Thus, it can be...

An exact asymptotic formula for the tail probability of a multivariate normal distribution is derived. This formula is applied to establish two asymptotic results for the maximum deviation from the mean: the weak convergence to the Gumbel distribution of a normalized maximum deviation and the...

Assuming that X1, ..., Xn is a random sample of lifetimes from a distribution with density [latin small letter f with hook] subject to random right-censoring, an estimator of the score function. [latin small letter f with hook]'(x)/[latin small letter f with hook](x), is then proposed and proved...