Ridge Estimation of the Inverse of a Covariance Matrix.
WYOMING UNIV LARAMIE STATISTICS LAB
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In many situations the standard estimators for the inverse of a covariance matrix from a normal population provide unsatisfactory results. Proposed as an alternative is a random matrix which undergoes an adjustment similar to that undergone by the normal equations matrix in ridge regression. This ridge adjustment is justified by appealing to the spectral decomposition of the inverse of the sample covariance matrix, the bias in the estimators of the characteristic roots of this matrix, and a Monte Carlo simulation. The ridge adjusted estimator is shown to be superior in many cases, especially, for small sample sizes.
- Statistics and Probability