This paper develops the theory of density estimation on the Stiefel manifoldVk, m, whereVk, mis represented by the set ofm-kmatricesXsuch thatX'X=Ik, thek-kidentity matrix. The density estimation by the method of kernels is considered, proposing two classes of kernel density estimators...

Motivated by the notion of regression depth (Rousseeuw and Hubert, 1996) we introduce thecatline, a new method for simple linear regression. At any bivariate data setZn={(xi, yi);i=1, ..., n} its regression depth is at leastn/3. This lower bound is attained for data lying on a convex or...

This paper proposes nonparametric deconvolution density estimation overS2. Here we would think of theS2elements of interest being corrupted by randomSO(3) elements (rotations). The resulting density on the observations would be a convolution of theSO(3) density with the trueS2density....

This paper provides computable representations for the evaluation of the probability content of cones in isotropic random fields. A decomposition of quadratic forms in spherically symmetric random vectors is obtained and a representation of their moments is derived in terms of finite sums. These...

In some long term studies, a series of dependent and possibly censored failure times may be observed. Suppose that the failure times have a common marginal distribution function having a density, and the nonparametric estimation of density and hazard rate under random censorship is of our...

We study the loss of information (measured in terms of the Kullback-Leibler distance) caused by observing "grouped" data (observing only a discretized version of a continuous random variable). We analyze the asymptotical behaviour of the loss of information as the partition becomes finer. In the...

This paper examines the role of Stein estimation in a linear ultrastructural form of the measurement errors model. It is demonstrated that the application of Stein rule estimation to the matrix of true values of regressors leads to the overcoming of the inconsistency of the least squares...

Consider a long term study, where a series of possibly censored failure times is observed. Suppose the failure times have a common marginal distribution functionF, but they exhibit a mode of dependence characterized by positive or negative association. Under suitable regularity conditions, it is...

Based on concentration probability of estimators about a true parameter, third-order asymptotic efficiency of the first-order bias-adjusted MLE within the class of first-order bias-adjusted estimators has been well established in a variety of probability models. In this paper we consider the...

In a previous investigation we studied some asymptotic properties of the sample mean location on submanifolds of Euclidean space. The sample mean location generalizes least squares statistics to smooth compact submanifolds of Euclidean space. In this paper these properties are put into use....