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

作者：Delicado Pedro^*; Smrekar Marcelo

来源：Statistics and Computing, 2009, 19(3): 255-269.

DOI：10.1007/s11222-008-9090-y

• Dependence measures
• Independence tests
• Linearity tests
• Principal curves
• Renyi's axioms
• Similarity measures for pairs of variables

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.

• 出版日期2009-9