Nonparametric Simulation Extrapolation for Measurement Error Models

TL;DR

This paper introduces a nonparametric extension of the SIMEX method for measurement error correction, allowing for more flexible application in non-normal error settings without assuming specific error distributions.

Contribution

The paper develops a nonparametric SIMEX approach that removes the need for normality assumptions, broadening the applicability of measurement error correction techniques.

Findings

Effective correction in non-normal error scenarios

Applicable with validation data or replicates

No distributional assumptions required

Abstract

The presence of measurement error is a widespread issue which, when ignored, can render the results of an analysis unreliable. Numerous corrections for the effects of measurement error have been proposed and studied, often under the assumption of a normally distributed, additive measurement error model. One such method is simulation extrapolation, or SIMEX. In many situations observed data are non-symmetric, heavy-tailed, or otherwise highly non-normal. In these settings, correction techniques relying on the assumption of normality are undesirable. We propose an extension to the simulation extrapolation method which is nonparametric in the sense that no specific distributional assumptions are required on the error terms. The technique is implemented when either validation data or replicate measurements are available, and is designed to be immediately accessible for those familiar with simulation extrapolation.