Multivariate regression with measurement error: bias analysis and estimation

Jingyu Cui and Grace Y. Yi

Journal of Nonparametric Statistics, 2025, vol. 37, issue 4, 1257-1297

Abstract: Multivariate regression models are commonly used to examine associations in multivariate data, and various methods have been proposed to characterise distinct features of such data across different settings. The validity of those methods, however, is compromised by the presence of measurement error. Despite extensive research on measurement error in univariate data, the impact of measurement error on the analysis of multivariate data remains an interesting topic to explore. This paper rigorously examines the measurement error effects on multivariate regression models and quantifies the asymptotic bias and covariance matrix for the naïve method that ignores measurement error. We further develop three estimation methods to correct the measurement error effects under different scenarios, including the case with instrument variables. The asymptotic properties of these methods are established accordingly. Lastly, extensions that apply nonparametric techniques to investigate the relationship between responses and covariates contaminated by measurement error are discussed.

Date: 2025
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DOI: 10.1080/10485252.2025.2540308

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