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2020 Assessing prediction error at interpolation and extrapolation points
Assaf Rabinowicz, Saharon Rosset
Electron. J. Statist. 14(1): 272-301 (2020). DOI: 10.1214/19-EJS1666

Abstract

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 $Loss(w_{t})$ 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 $C_{p}$ 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.

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Assaf Rabinowicz. Saharon Rosset. "Assessing prediction error at interpolation and extrapolation points." Electron. J. Statist. 14 (1) 272 - 301, 2020. https://doi.org/10.1214/19-EJS1666

Information

Received: 1 September 2018; Published: 2020
First available in Project Euclid: 8 January 2020

zbMATH: 07154989
MathSciNet: MR4048600
Digital Object Identifier: 10.1214/19-EJS1666

Keywords: $AIC$ , expected optimism , kriging , linear mixed models , model assessment , Model selection

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Vol.14 • No. 1 • 2020
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