Debiased inference in error-in-variable problems with non-Gaussian measurement error

TL;DR

This paper introduces a novel method using hypercomplex numbers to reduce bias in statistical inference when data is contaminated with non-Gaussian measurement error, outperforming traditional Gaussian-based approaches.

Contribution

The paper proposes a new bias reduction technique leveraging hypercomplex numbers for error-in-variable problems with non-Gaussian errors, applicable to various regression models and density estimation.

Findings

Significant bias reduction demonstrated in simulations

Effective application to sports analytics data

Outperforms Gaussian-based methods in non-Gaussian settings

Abstract

We consider drawing statistical inferences based on data subject to non-Gaussian measurement error. Unlike most existing methods developed under the assumption of Gaussian measurement error, the proposed strategy exploits hypercomplex numbers to reduce bias in naive estimation that ignores non-Gaussian measurement error. We apply this new method to several widely applicable parametric regression models with error-prone covariates, and kernel density estimation using error-contaminated data. The efficacy of this method in bias reduction is demonstrated in simulation studies and a real-life application in sports analytics.