Electronic Journal of Statistics

Prediction in abundant high-dimensional linear regression

R. Dennis Cook, Liliana Forzani, and Adam J. Rothman

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An abundant regression is one in which most of the predictors contribute information about the response, which is contrary to the common notion of a sparse regression where few of the predictors are relevant. We discuss asymptotic characteristics of methodology for prediction in abundant linear regressions as the sample size and number of predictors increase in various alignments. We show that some of the estimators can perform well for the purpose of prediction in abundant high-dimensional regressions.

Article information

Electron. J. Statist., Volume 7 (2013), 3059-3088.

First available in Project Euclid: 16 December 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62J05: Linear regression
Secondary: 62H12: Estimation

Inverse regression least squares Moore-Penrose inverse sparse covariance estimation


Cook, R. Dennis; Forzani, Liliana; Rothman, Adam J. Prediction in abundant high-dimensional linear regression. Electron. J. Statist. 7 (2013), 3059--3088. doi:10.1214/13-EJS872. https://projecteuclid.org/euclid.ejs/1387207935

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