Exploration of Distributions of Ratio of Partial Sum of Sample Eigenvalues When All Population Eigenvalues Are the Same

• Activity Number: 321
• Type: Contributed
• Date/Time: Wednesday, August 14, 2002 : 12:00 PM to 1:50 PM
• Sponsor: Section on Statistical Graphics*
• Author(s): Moonseong Heo*+
• Affiliation(s): Weill Medical College of Cornell University
• Keywords: Bias ; Biplot ; Eigenvalues ; Multivariate Gaussian distribution

Abstract

This paper explores empirically the first two moments of ratio of the partial sum of the first two sample eigenvalues to the sum of all eigenvalues when the population eigenvalues of a covariance matrix are all the same. For a data matrix X with order n-by-m element-wise independent normal distribution with mean 0 and non-zero variance is assumed. Exact and large sample asymptotic distributions of the sample ratios under this situation are reviewed. Biases and standard deviations of the sample ratios are empirically obtained from simulations within a range of order of the data matrix and then fitted on the basis of the biplot graphical diagnosis proposed by Bradu and Gabriel (1976). Use of the estimated first two moments in assessing goodness of fit of graphical displays is briefly discussed.