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We propose a novel approach to the analysis of covariance operators making use of concentration inequalities. First, non-asymptotic confidence sets are constructed for such operators. Then, subsequent applications including a k sample test for equality of covariance, a functional data classifier, and an expectation-maximization style clustering algorithm are derived and tested on both simulated and phoneme data.
The assumption of separability of the covariance operator for a random image or hypersurface can be of substantial use in applications, especially in situations where the accurate estimation of the full covariance structure is unfeasible, either for
Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization by V. Koltchinskii [arXiv:0708.0083]
Distribution function is essential in statistical inference, and connected with samples to form a directed closed loop by the correspondence theorem in measure theory and the Glivenko-Cantelli and Donsker properties. This connection creates a paradig
For testing two random vectors for independence, we consider testing whether the distance of one vector from a center point is independent from the distance of the other vector from a center point by a univariate test. In this paper we provide condit
Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature, there have be