Accession Number : AD0259024

Title :   ASYMPTOTIC THEORY FOR PRINCIPAL COMPONENT ANALYSIS

Corporate Author : COLUMBIA UNIV NEW YORK

Personal Author(s) : ANDERSON,T.W.

Report Date : 03 FEB 1961

Pagination or Media Count : 57

Abstract : The asymptotic distribution of the characteristic roots and (normalized) vectors of a sample covariance matrix is given when the observations are from a multivariate normal distribution whose covariance matrix has characteristic roots of arbitrary multiplicity. The elements of each characteristic vector are the coefficients of a principal component (with sum of squares of coefficients being unity), and the corresponding characteristic root is the variance of the principal component. Tests of hypotheses of equality of population roots are treated, and confidence intervals for assumed equal roots are given; these are useful in assessing the importance of principal components. A similar study for correlation matrices is considered. (Author)

Descriptors :   *ANALYSIS OF VARIANCE, *STATISTICAL ANALYSIS, *STATISTICAL FUNCTIONS, MATRICES(MATHEMATICS), MEASURE THEORY, PROBABILITY, SAMPLING, STATISTICAL DISTRIBUTIONS

Distribution Statement : APPROVED FOR PUBLIC RELEASE