Assessing Prediction Error at Interpolation and Extrapolation Points

TL;DR

This paper introduces new prediction error estimators, tAI and Loss(w_t), designed for assessing model prediction accuracy at interpolation and extrapolation points, where traditional in-sample error measures are inadequate.

Contribution

The paper proposes novel prediction error estimators and model selection criteria applicable to interpolation and extrapolation scenarios, extending beyond traditional in-sample error-based methods.

Findings

New estimators perform well in simulations

Methods effectively assess prediction error at extrapolation points

Demonstrated advantages in real data analysis within Linear Mixed Models

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 cannot be used for estimating the 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 the prediction error estimators, two model selection criteria with the same spirit as $AIC$ are suggested. The advantages of our suggested methods are demonstrated in simulation and real data analysis of studies involving interpolation and extrapolation in a Linear Mixed Model framework.