A Comparison between robust methods in canonical correlation by using empirical influence function

Abstract

       Canonical correlation analysis is one of the common methods for analyzing data and know the relationship between two sets of variables under study, as it depends on the process of analyzing the variance matrix or the correlation matrix. Researchers resort to the use of many methods to estimate canonical correlation (CC); some are biased for outliers, and others are resistant to those values; in addition, there are standards that check the efficiency of estimation methods.

In our research, we dealt with robust estimation methods that depend on the correlation matrix in the analysis process to obtain a robust canonical correlation coefficient, which is the method of Biweight Midcorrelation coefficient (Bi) and Kendall-tau correlation coefficient (Ke).

From the comparison between these two methods through the empirical influence function with standard scaled and transformed estimator, the results indicated the efficiency and the preference of the (Bi) method. The study also has application with real data followed a multivariate normal distribution with two sets; the first group represents monthly averages for quantities of exported oil from three OPEC countries, namely Saudi Arabia, Iraq, and Kuwait, the other group represents the returns of those quantities for the period from 2015 to 2019, after applied (Bi) method and estimate IF, the strongest influence about CC was at thirty four-months and the lowest was at twenty-seven