Canonical Correlation Analysis for Three Sets of Variables under Non-linearity and Skew-normally Distributed Conditions

This paper examines the performance of two methods of parameter estimation namely Hotelling procedure and Kendal procedure against a newly proposed method in canonical correlation model for three data sets under nonlinearity and skew-normally distributed assumptions. Estimates of the parameters were obtained and compared using Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC). Simulation study was carried out for the least possible case in Canonical Correlation Analysis (CCA), in which there are two variables in the three data sets, that is, X = (X1, X2), Y = (Y1, Y2) and Z = (Z1,Z2). 8 levels of skewness and 5 degrees of nonlinearity were mixed to give 40 combinations of synthetic datasets. Each degree of nonlinearity represents a nonlinear function. The functions were selected such as to represent the basic nonlinear models that are usually seen in real-life applications. Results obtained showed that Hotelling procedure and the proposed gave exact and correct values of p for case of linearity but differ slightly for case of nonlinearity while the Kendal gave p values that are far away from the true p values for different degrees of nonlinearity and different levels of Skewness.