The Asymptotic Equivalence of Ridge and Principal Component Regression with Many Predictors
Econometrics and Statistics, 2024
Lucrezia Reichlin, Christine De Mol, Domenico Giannone
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.
Citation:
The Asymptotic Equivalence of Ridge and Principal Component Regression with Many Predictors (with C. De Mol and D. Giannone), Econometrics and Statistics, in press, 2024.
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