Review Article Open Access

Explaining the Generalized Cross-Validation on Linear Models

Lucas Monteiro Chaves1, Laerte Dias de Carvalho1, Carlos José dos Reis1 and Devanil Jaques de Souza1
  • 1 Federal University of Lavras, Brazil

Abstract

Cross-Validation is a model validation method widely used by the scientific community. The Generalized Cross-Validation (GCV) is an invariant version of the usual Cross-Validation method. This generalization was obtained using the non usual theory of circulant complex matrices. In this work we intend to give a clear and complete exposition concerning the linear algebra assumptions required by the theory. The aim was to make this text accessible to a wide audience of statisticians and non-statisticians who use the Cross-Validation method in their research activities. It is also intended to supply the absence of a basic reference on this topic in the literature.

Journal of Mathematics and Statistics
Volume 15 No. 1, 2019, 298-307

DOI: https://doi.org/10.3844/jmssp.2019.298.307

Submitted On: 1 July 2019 Published On: 25 October 2019

How to Cite: Chaves, L. M., Carvalho, L. D. D., Reis, C. J. D. & Souza, D. J. D. (2019). Explaining the Generalized Cross-Validation on Linear Models. Journal of Mathematics and Statistics, 15(1), 298-307. https://doi.org/10.3844/jmssp.2019.298.307

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Keywords

  • Circulant Matrices
  • PRESS Statistics
  • Prediction Error