R-estimation of optimal transformations via copulas and ACE

Abstract

This paper investigates a rank-based ACE-algorithm using orthonormal polynomial regression. It is a modification of an R-estimation procedure for finding maximally correlated data transformations (cf. Rödel, 1989). Both methods are consistent and are compared by examples.

Keywords:

• Bivariate distributions
• Copulas
• Rank-based estimation
• Alternating conditional expectation
• Density estimation
• Polynomial smoothing
• Generalized cross validation
• Maximal correlation
• Stochastically increasing random variables