Distribución del cuadrado de la máxima correlación canónica para tamaños muestrales pequeños

María R. SANTILLÁN and Aldo J. VIOLLAZ

ABSTRACT

Assume that the normally distributed random vector of components is partitioned into two subvectors and of and components respectively. Suppose also that the two subvectors are not correlated. In this work we study the distribution of the largest squared canonical correlation when , and the number of observations in the sample , are rather small. We give the explicit expressions of the cumulative distribution functions and the computed values of the sample mean and variance of . We prove that there exists a stochastic order between the largest squared canonical correlations obtained from two different partitions of the vector . More precisely, increase stochastically when the difference between and decrease. Since and are uncorrelated the largest squared canonical correlation in the population is zero. Therefore the mean of is the bias of when is used to estimate . The values of the mean and the variance show that the square of the bias is bigger than the variance in all the cases.

1980 Mathematics Subject Classification (1985 revision): 46E35