The Asymptotic Equivalence of Ridge and Principal Component Regression with Many Predictors

Abstract

The asymptotic properties of ridge regression in large dimension are studied. Two key results are established. First, consistency and rates of convergence for ridge regression are obtained under assumptions which impose different rates of increase in the dimension n between the first n1 and the remaining n−n1 eigenvalues of the population covariance of the predictors. Second, it is proved that under the special and more restrictive case of an approximate factor structure, principal component and ridge regression have the same rate of convergence and the rate is faster than the one previously established for ridge.