Wavelets-Based Estimation of Nonlinear Canonical Analysis

Using a wavelets-based estimator of the bivariate density, we introduce an estimation method for nonlinear canonical analysis. Consistency of the resulting estimators of the canonical coefficients and the canonical functions is established. Under some conditions, asymptotic normality results for these estimators are obtained. Then it is shown how to compute in practice these estimators by using matrix computations, and the finite-sample performance of the proposed method is evaluated through simulations.