The concept of data depth leads to a center-outward ordering of multivariate data, and it has been effectively used for developing various data analytic tools. While different notions of depth were originally developed for finite dimensional data, there have been some recent attempts to develop...

Over the last couple of decades, data depth has emerged as a powerful exploratory and inferential tool for multivariate data analysis with wide-spread applications. This paper investigates the possible use of different notions of data depth in non-parametric discriminant analysis. First, we...

Let (X, Y) be a random vector such that X is d-dimensional, Y is real valued, and [theta](X) is the conditional [alpha]th quantile of Y given X, where [alpha] is a fixed number such that 0 < [alpha] < 1. Assume that [theta] is a smooth function with order of smoothness p > 0, and set r = (p - m)/(2p + d), where m is a nonnegative integer smaller than p. Let T([theta]) denote a...</[alpha]>

A modified version of the usual M-estimation problem is proposed, and sample median is shown to be a solution of this problem for a wide range of choices of the score function. It exposes certain universality in the robustness of sample median in the univariate case, and this property continues...

A likelihood-based generalization of usual kernel and nearest-neighbor-type smoothing techniques and a related extension of the least-squares leave-one-out cross-validation are explored in a generalized regression set up. Several attractive features of the procedure are discussed and asymptotic...

The need for comparing two regression functions arises frequently in statistical applications. Comparison of the usual regression functions is not very meaningful in situations where the distributions and the ranges of the covariates are different for the populations. For instance, in...