Assessing prediction error at interpolation and extrapolation points

Assaf Rabinowicz, Saharon Rosset

Research output: Contribution to journalArticlepeer-review


Common model selection criteria, such as AIC and its variants, are based on in-sample prediction error estimators. However, in many applications involving predicting at interpolation and extrapolation points, in-sample error does not represent the relevant prediction error. In this paper new prediction error estimators, tAI and Loss(wt) are introduced. These estimators generalize previous error estimators, however are also applicable for assessing prediction error in cases involving interpolation and extrapolation. Based on these prediction error estimators, two model selection criteria with the same spirit as AIC and Mallow’s Cp are suggested. The advantages of our suggested methods are demonstrated in a simulation and a real data analysis of studies involving interpolation and extrapolation in linear mixed model and Gaussian process regression.

Original languageEnglish
Pages (from-to)272-301
Number of pages30
JournalElectronic Journal of Statistics
Issue number1
StatePublished - 2020


  • AIC
  • Expected optimism
  • Kriging
  • Linear mixed models
  • Model assessment
  • Model selection

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'Assessing prediction error at interpolation and extrapolation points'. Together they form a unique fingerprint.

Cite this