Approximate maximum likelihood estimators for linear regression with independent component-wise design matrix uncertainty

  • In this paper we consider regression problems subject to noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been studied extensively for ordinary/total least squares, and via models that implicitly or explicitly assume Gaussianity, less attention has been paid to improving estimation for regression problems under general independent component-wise uncertainty in the design matrix. To address difficulties encountered when dealing with distributions of sums of random variables, we rely on the saddle point method to estimate densities and form an approximate log-likelihood to maximize. We show that the proposed method performs favorably against other classical methods.

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Metadaten
Author:Richard J. Clancy, Stephen Becker
DOI:https://doi.org/10.1007/s12532-024-00268-6
ISSN:1867-2949
Parent Title (English):Mathematical Programming Computation
Publisher:Springer Science and Business Media LLC
Document Type:Article
Language:English
Year of Completion:2024
Volume:17
Issue:1
Page Number:27
First Page:53
Last Page:79
Mathematical Programming Computation :MPC 2025 - Issue 1
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