🤖 AI Summary
Conventional statistical inference suffers from bias under non-Gaussian measurement errors, violating the classical Gaussian error assumption. Method: This paper proposes a novel debiasing framework grounded in hypercomplex algebra—marking the first application of hypercomplex numbers to measurement error modeling. By explicitly representing and correcting non-Gaussian error structures, the method relaxes restrictive distributional assumptions. It unifies treatment across parametric regression and kernel density estimation, delivering unbiased or nearly unbiased inference under contaminated data. Contribution/Results: Theoretical analysis establishes consistency and asymptotic normality; extensive simulations and real-world sports analytics data demonstrate substantial gains in estimation accuracy, robustness to error distribution misspecification, and practical applicability. The approach offers an interpretable, generalizable paradigm for errors-in-variables problems, advancing beyond traditional moment-based or simulation-extrapolation techniques.
📝 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.