On the asymptotic risk of ridge regression with many predictors

Article Type

Research Article

Publication Title

Indian Journal of Pure and Applied Mathematics

Abstract

This work is concerned with the properties of the ridge regression where the number of predictors p is proportional to the sample size n. Asymptotic properties of the means square error (MSE) of the estimated mean vector using ridge regression is investigated when the design matrix X may be non-random or random. Approximate asymptotic expression of the MSE is derived under fairly general conditions on the decay rate of the eigenvalues of XTX when the design matrix is nonrandom. The value of the optimal MSE provides conditions under which the ridge regression is a suitable method for estimating the mean vector. In the random design case, similar results are obtained when the eigenvalues of E[XTX] satisfy a similar decay condition as in the non-random case.

First Page

1040

Last Page

1054

DOI

10.1007/s13226-024-00646-9

Publication Date

9-1-2024

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