A note on the prediction error of principal component regression

2018/11/07 by Martin Wahl, Wahl, Martin
Computer Science · Mathematics · #62H25 #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1811.02998

openalex publication_date 2018/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyse the prediction error of principal component regression (PCR) and prove non-asymptotic upper bounds for the corresponding squared risk. Under mild assumptions, we show that PCR performs as well as the oracle method obtained by replacing empirical principal components by their population counterparts. Our approach relies on upper bounds for the excess risk of principal component analysis.

Citations

• Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators

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