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