Measuring non-linear dependence for two random variables distributed along a curve
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We propose new dependence measures for two real random variables not necessarily linearly related. Covariance and linear correlation are expressed in terms of principal components and are generalized for variables distributed along a curve. Properties of these measures are discussed. The new measures are estimated using principal curves and are computed for simulated and real data sets. Finally, we present several statistical applications for the new dependence measures.
KeywordsDependence measures Independence tests Linearity tests Principal curves Rényi’s axioms Similarity measures for pairs of variables
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