Canonical correlation coefficients of high-dimensional Gaussian vectors: Finite rank case

High-dimensional Approximations of the Coefficients on Linear Dis- criminant Functions and Canonical Correlation Variates

For discriminant analysis with (q + 1) p-dimensional populations, most inferential problems are based on two matrices Sb and Sw of sums of squares and products due to between-groups and withingroups, respectively. In this paper we are interesting in asymptotic behaviors of the coefficients on the linear discriminant functions, which are the characteristic vectors of S−1 w Sb. Under normality Sb...

Independence Test For High Dimensional Data Based On Regularized Canonical Correlation Coefficients

This paper proposes a new statistic to test independence between two high dimensional random vectors x : p1× 1 and y : p2× 1. The proposed statistic is based on the sum of regularized sample canonical correlation coefficients of x and y. The asymptotic distribution of the statistic under the null hypothesis is established as a corollary of general central limit theorems (CLT) for the linear sta...

Autoregressive Gaussian Random Vectors of First Order

Gaussian processes for canonical correlation analysis

We consider several stochastic process methods for performing canonical correlation analysis (CCA). The first uses a Gaussian Process formulation of regression in which we use the current projection of one data set as the target for the other and then repeat in the opposite direction. The second uses a method which relies on probabilistically sphering the data, concatenating the two streams and...

The Gaussian rank correlation estimator: robustness properties

The Gaussian rank correlation equals the usual correlation coefficient computed from the normal scores of the data. Although its influence function is unbounded, it still has attractive robustness properties. In particular, its breakdown point is above 12%. Moreover, the estimator is consistent and asymptotically efficient at the normal distribution. The correlation matrix obtained from pairwis...