Measuring non-linear dependence for two random variables distributed along a curve

Authors:
Pedro Delicado;Marcelo Smrekar
Affiliations:
Departament d'Estadística i Investigació Operativa, Universitat Politècnica de Catalunya, Barcelona, Spain 08034;Departament d'Estadística i Investigació Operativa, Universitat Politècnica de Catalunya, Barcelona, Spain 08034
Venue:
Statistics and Computing
Year:
2009

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Abstract

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.