Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series B, Pt. 2, 215--220

INFERENCES RELATING TO THE MULTIPLICITY OF THE SMALLEST EIGENVALUE OF A CORRELATION MATRIX

By

JAMES R. SCHOTT
* University of Central Florida, Orlando*

SUMMARY. The minimum chi-squared test is obtained for testing the hypothesis that the smallest r eigenvalues of an m x m correlation matrix are equal, where r < m is specified in advance. One advantage of this test is that it provides as a natural byproduct a correlation matrix estimator that has multiplicity r for its smallest eigenvalue.

*AMS (1991) subject classification.*62H15, 62H12.

*Key words and phrases. *Minimum chi-squared estimator;
minimum chi-squared test; principal components analysis;