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Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation, distance correlation is zero only if the random vectors are independent. The empirical distance dependence measures are based on certain Euclidean distances between sample elements rather than sample moments, yet have a compact representation analogous to the classical covariance and correlation. Asymptotic properties and applications in testing independence are discussed. Implementation of the test and Monte Carlo results are also presented.
The Gaussian model equips strong properties that facilitate studying and interpreting graphical models. Specifically it reduces conditional independence and the study of positive association to determining partial correlations and their signs. When G
We discuss a general approach to handling multiple hypotheses testing in the case when a particular hypothesis states that the vector of parameters identifying the distribution of observations belongs to a convex compact set associated with the hypot
Rejecting the null hypothesis in two-sample testing is a fundamental tool for scientific discovery. Yet, aside from concluding that two samples do not come from the same probability distribution, it is often of interest to characterize how the two di
This work builds a unified framework for the study of quadratic form distance measures as they are used in assessing the goodness of fit of models. Many important procedures have this structure, but the theory for these methods is dispersed and incom
In this paper, we develop Bayes and maximum a posteriori probability (MAP) approaches to monotonicity testing. In order to simplify this problem, we consider a simple white Gaussian noise model and with the help of the Haar transform we reduce it to