A note on the prediction error of principal component regression in high dimensions
Hucker L, Wahl M (2023)
Theory of Probability and Mathematical Statistics 109: 37-53.
Zeitschriftenaufsatz
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Autor*in
Hucker, Laura;
Wahl, MartinUniBi
Einrichtung
Abstract / Bemerkung
We analyze the prediction error of principal component regression (PCR) and prove high probability bounds for the corresponding squared risk conditional on the design. Our first main result shows that PCR performs comparably to the oracle method obtained by replacing empirical principal components by their population counterparts, provided that an effective rank condition holds. On the other hand, if the latter condition is violated, then empirical eigenvalues start to have a significant upward bias, resulting in a self-induced regularization of PCR. Our approach relies on the behavior of empirical eigenvalues, empirical eigenvectors and the excess risk of principal component analysis in high-dimensional regimes.
Erscheinungsjahr
2023
Zeitschriftentitel
Theory of Probability and Mathematical Statistics
Band
109
Seite(n)
37-53
ISSN
0094-9000
eISSN
1547-7363
Page URI
https://pub.uni-bielefeld.de/record/2969764
Zitieren
Hucker L, Wahl M. A note on the prediction error of principal component regression in high dimensions. Theory of Probability and Mathematical Statistics . 2023;109:37-53.
Hucker, L., & Wahl, M. (2023). A note on the prediction error of principal component regression in high dimensions. Theory of Probability and Mathematical Statistics , 109, 37-53. https://doi.org/10.1090/tpms/1196
Hucker, Laura, and Wahl, Martin. 2023. “A note on the prediction error of principal component regression in high dimensions”. Theory of Probability and Mathematical Statistics 109: 37-53.
Hucker, L., and Wahl, M. (2023). A note on the prediction error of principal component regression in high dimensions. Theory of Probability and Mathematical Statistics 109, 37-53.
Hucker, L., & Wahl, M., 2023. A note on the prediction error of principal component regression in high dimensions. Theory of Probability and Mathematical Statistics , 109, p 37-53.
L. Hucker and M. Wahl, “A note on the prediction error of principal component regression in high dimensions”, Theory of Probability and Mathematical Statistics , vol. 109, 2023, pp. 37-53.
Hucker, L., Wahl, M.: A note on the prediction error of principal component regression in high dimensions. Theory of Probability and Mathematical Statistics . 109, 37-53 (2023).
Hucker, Laura, and Wahl, Martin. “A note on the prediction error of principal component regression in high dimensions”. Theory of Probability and Mathematical Statistics 109 (2023): 37-53.
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arXiv: 2212.04959
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