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A copula based differential measure of local correlation

By Daniel Bruynooghe

Abstract

A copula based measure of local correlation is developed for two random variables X and Y . The measure is originally motivated through the limiting process of a sequence of correlations in shrinking local neighbourhoods around (x, y). It is shown that this method is better applied in ‘copula space’ to the transformed variables FX(x), FY (y) in a sense of capturing the independence case properly. Upon transforming back via the inverse marginal CDFs, we arrive at a novel measure of local correlation. We illustrate its geometry for the bivariate Gaussian case. Finally, a non-parametric estimator is presented and its asymptotic distribution identified

Topics: QA Mathematics
Year: 2010
OAI identifier: oai:eprints.lse.ac.uk:28069
Provided by: LSE Research Online

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Citations

  1. (1996). Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems. doi

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