We present a procedure for the identification of clusters in multivariate data sets, based on the comparison between the k nearest neighbors graph, Gk, and the minimal spanning tree, MST. Our key statistic is the random quantity the smallest k such that Gk contains the MST. Under regularity...

We consider the problem of identifying the dimension in which a sample of data points lives, when only their interpoint distances are known. We study as a random variable the average "reach" of vertices in the k-nearest-neighbors graph associated to the interpoint distance matrix, and we show...

We present and study a procedure for testing the null hypothesis of multivariate elliptical symmetry. The procedure is based on the averages of some spherical harmonics over the projections of the scaled residual (1978, N. J. H. Small, Biometrika65, 657-658) of the d-dimensional data on the unit...

Rank procedures for parameter estimation in linear regression with current status data are introduced. The error distribution is not specified. The estimates are shown to be consistent using empirical processes theory for U-statistics.