Rank estimation by canonical correlation analysis in multivariate statistics has been proposed as an alternative approach for estimating the number of components in a multicomponent mixture. A methodological turning point of this new approach is that it focuses on the difference in structure rather than in magnitude in characterizing the difference between the signal and the noise. This structural difference is quantified through the analysis of canonical correlation, which is a well-established data reduction technique in multivariate statistics. Unfortunately, there is a price to be paid for having this structural difference: at least two replicate data matrices are needed to carry out the analysis.
In this paper we continue to explore the potential and to extend the scope of the canonical correlation technique. In particular, we propose a bootstrap resampling method which makes it possible to perform the canonical correlation analysis on a single data matrix. Since a robust estimator is introduced to make inference about the rank, the procedure may be applied to a wide range of data without any restriction on the noise distribution. Results from real as well as simulated mixture samples indicate that when used in conjunction with this resampling method, canonical correlation analysis of a single data matrix is equally efficient as of replicate data matrices.
KEY WORDS
Rank estimation
Bootstrap resampling Canonical correlation Excitation-emission matrix Singular value decomposition in the mixture. Most methods which have been proposed to estimate the rank in the presence of noise rely in essence on the information summarized by the eigenvalues from the singular value decomposition of the underlying matrix. ' -6 Even though it is difficult to evaluate the amount of information which is lost due to this type of data summary (or reduction), it is not very hard to convince oneself at least heuristically that some information is lost, since it ignores any information contained in the eigenvectors which may well provide much more information than the eigenvalues do. A different approach which also incorporates the information in the