2007/02/01 by R. Dennis Cook · 5 citations
Engineering · Mathematics · #Advanced Statistical Methods and Models #Artificial intelligence #Combinatorics #Computer science #Control Systems and Identification #Dimension (graph theory) #Dimensionality reduction #Econometrics #Limit (mathematics) #Mathematics #Principal (computer security) #Principal component analysis #Reduction (mathematics) #Regression #Regression analysis #Statistical Methods and Inference #Statistics #stat.ME
paper · pdf · doi:10.1214/088342306000000682
published as Statistical Science 2007, Vol. 22, No. 1, 1-26 · This paper commented in: [arXiv:0708.3776], [arXiv:0708.3777], [arXiv:0708.3779]. Rejoinder in [arXiv:0708.3781]. Published at http://dx.doi.org/10.1214/088342306000000682 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2007/02/01 · arxiv created 2007/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Beginning with a discussion of R. A. Fisher’s early written remarks that relate to dimension reduction, this article revisits principal components as a reductive method in regression, develops several model-based extensions and ends with descriptions of general approaches to model-based and model-free dimension reduction in regression. It is argued that the role for principal components and related methodology may be broader than previously seen and that the common practice of conditioning on observed values of the predictors may unnecessarily limit the choice of regression methodology.