We provide necessary and sufficient conditions for the validity of the inequality of Simes (1986) in models with elliptical dependencies. Necessary conditions are presented in terms of sufficient conditions for the reverse Simes inequality. One application of our main results concerns the problem of model misspecification, in particular the case that the assumption of Gaussianity of test statis...

Censored quantile regressions have received a great deal of attention in the literature. In a linear setup, recent research has found that an estimator based on the idea of “redistribution-of-mass” (Efron, 1967) has better numerical performance than other available methods. In this paper, this idea is combined with the local polynomial kernel smoothing for nonparametric quantile regression of c...

In this paper, we presented a theoretical result and then discussed possible applications of our result to SDR problems. In addition to providing insights into existing SDR methods when Y is univariate; our theorem also applies to multivariate responses, especially when the response takes the form of ðY ;W Þ, where Y is a continuous variable and W is categorical. r 2007 Elsevier B.V. All rights...

Sufficient dimension reduction aims at finding transformations of predictor X without losing any regression information of Y versus X . If we are only interested in the information contained in the mean function or the kth moment function of Y given X , estimation of the central mean space or the central kth moment space becomes our focus. However, existing estimators for the central mean space...

In this paper we address the problem of learning Support Vector Machine (SVM) classifiers from distributed data sources. We identify sufficient statistics for learning SVMs and present an algorithm that learns SVMs from distributed data by iteratively computing the set of sufficient statistics. We prove that our algorithm is exact with respect to its centralized counterpart and efficient in ter...

The purpose of this paper is twofold: i) to introduce the sufficient statistic algebra which is responsible for propagating the sufficient statistics, or information state, in the optimal control of stochastic systems and ii) to apply certain Lie algebraic methods and gauge transformations, widely used in nonlinear control theory and quantum physics, to derive new results concerning finite-dime...