We consider a simple general construct, that of marginal replacement in a multivariate distribution, that provides, in particular, an interesting way of producing distributions that have a skew marginal from spherically symmetric starting points. Particular examples include a new multivariate...

Varying coefficient models are useful extensions of the classical linear models. Under the condition that the coefficient functions possess about the same degrees of smoothness, the model can easily be estimated via simple local regression. This leads to the one-step estimation procedure. In...

The current study provides a simple algorithm for finding the optimal ROC curve for a linear discriminant between two point distributions, given only information about the classes' means and covariances. The method makes no assumptions concerning the exact type of distribution and is shown to...

We introduce bivariate quantiles which are defined through the bivariate distribution function. This approach ensures that, unlike most multivariate medians or the multivariate M-quartiles, the bivariate quantiles satisfy an analogous property to that of the univariate quantiles in that they...

Consider the Kaplan-Meier estimate of the distribution function for right randomly censored data. We show that a U-statistic defined via this estimate is asymptotically normal. Under a condition of degeneracy, different from the degeneracy condition in uncensored models, it has an asymptotic...

We consider the problem of estimating jump points in smooth curves. Observations (Xi,Yi) i=1,...,n from a random design regression function are given. We focus essentially on the basic situation where a unique change point is present in the regression function. Based on local linear regression,...

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...

It is well known that the sample covariance is not an efficient estimator of the covariance of a bivariate normal vector. We extend this result to elliptical distributions and we propose a simple explicit estimator, which is efficient in the normal case and which outperforms the sample...

This paper addresses the issue of optimal deconvolution density estimation on the 2-sphere. Indeed, by using the transitive group action of the rotation matrices on the 2-dimensional unit sphere, rotational errors can be introduced analogous to the Euclidean case. The resulting density turns out...

In this paper we extend the definition of the influence function to functionals of more than one distribution, that is, for estimators depending on more than one sample, such as the pooled variance, the pooled covariance matrix, and the linear discriminant analysis coefficients. In this case the...