Prediction in Measurement Error Models

TL;DR

This paper develops a method for constructing prediction intervals in measurement error models that are accurate and robust, even when the underlying distributional assumptions are incorrect, with applications to biomedical data.

Contribution

It introduces a novel approach to prediction interval estimation in measurement error models that is consistent under model misspecification and provides practical guidance on interval length optimization.

Findings

Prediction intervals achieve the desired coverage levels.

Method remains consistent under incorrect model assumptions.

Numerical experiments demonstrate effectiveness in real data.

Abstract

We study the well known difficult problem of prediction in measurement error models. By targeting directly at the prediction interval instead of the point prediction, we construct a prediction interval by providing estimators of both the center and the length of the interval which achieves a pre-determined prediction level. The constructing procedure requires a working model for the distribution of the variable prone to error. If the working model is correct, the prediction interval estimator obtains the smallest variability in terms of assessing the true center and length. If the working model is incorrect, the prediction interval estimation is still consistent. We further study how the length of the prediction interval depends on the choice of the true prediction interval center and provide guidance on obtaining minimal prediction interval length. Numerical experiments are conducted to illustrate the performance and we apply our method to predict concentration of Abeta1-12 in cerebrospinal fluid in an Alzheimer's disease data.