Statistics and Computing

, Volume 10, Issue 3, pp 209–229

On the use of cross-validation to assess performance in multivariate prediction


  • P. Jonathan
    • Shell Research Ltd.
  • W. J. Krzanowski
    • School of Mathematical SciencesUniversity of Exeter
  • W. V. McCarthy
    • Shell Research Ltd.

DOI: 10.1023/A:1008987426876

Cite this article as:
Jonathan, P., Krzanowski, W.J. & McCarthy, W.V. Statistics and Computing (2000) 10: 209. doi:10.1023/A:1008987426876


We describe a Monte Carlo investigation of a number of variants of cross-validation for the assessment of performance of predictive models, including different values of k in leave-k-out cross-validation, and implementation either in a one-deep or a two-deep fashion. We assume an underlying linear model that is being fitted using either ridge regression or partial least squares, and vary a number of design factors such as sample size n relative to number of variables p, and error variance. The investigation encompasses both the non-singular (i.e. n > p) and the singular (i.e. n ≤ p) cases. The latter is now common in areas such as chemometrics but has as yet received little rigorous investigation. Results of the experiments enable us to reach some definite conclusions and to make some practical recommendations.

cross-validationridge regressionpartial least squarespredictionassessment of predictive models

Copyright information

© Kluwer Academic Publishers 2000