Sankhya: The Indian Journal of Statistics

1993, Volume 55, Series B, Pt. 3, 353--371

FINITE SAMPLE PROPERTIES OF A MEASURE OF MULTICOLLINEARITY

By

J. S. MEHTA, *Temple University, U.S.A*

P. A. V. B. SWAMY, *Federal Reserve Board, U. S. A.*

And

N. S. IYENGAR, *Indian Statistical Institute, Bangalore*

SUMMARY. This article deals with exact finite sample properties of a summary statistic that is used to measure the effects of multicollinearity on the contributions of regressors to the square of the multiple correlation coefficient of a regression and with the regressors. This statistic measures the "distance" of a cross-product matrix from the diagonal matrix obtained by zeroing its off-diagonal elements and hence is useful in detecting near multicollinearities in regression problems. It can also distinguish between apparent and real multicollinearities with positive probability.

*Subject classification*. 62J05