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

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 rema...

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Bibliographic Details
Published inEconometrics and statistics
Main Authors De Mol, Christine, Giannone, Domenico, Reichlin, Lucrezia
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.03.2024
Subjects
Asymptotic inference
Factor models
Forecasting
High-dimensional time series
Ridge regression
Ridge regression
Factor models
Asymptotic inference
High-dimensional time series
Forecasting
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Summary: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.
ISSN:2452-3062
2452-3062
DOI:10.1016/j.ecosta.2024.02.005