Linear Model Estimation and Prediction for p > n

Ronald Christensen

The American Statistician, 2026, vol. 80, issue 2, 232-240

Abstract: We consider ordinary least squares estimation and variations on least squares estimation such as penalized (regularized) least squares and spectral shrinkage estimates for problems with p>n and associated problems with prediction of new observations. After the introduction of Section 1, Section 2 examines a number of commonly used estimators for p>n. Section 3 introduces prediction with p>n. Section 4 introduces notational changes to facilitate discussion of overfitting and Section 5 illustrates the phenomenon of double descent. We conclude with some final comments.

Date: 2026
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DOI: 10.1080/00031305.2025.2566251

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