Nonexistence of Maximum Likelihood Estimation of Variance Components in Some Stochastic Models
Publication: Journal of Surveying Engineering
Volume 146, Issue 2
Abstract
Although maximum likelihood has been widely used to estimate unknown parameters in stochastic models of random errors, we show that the method cannot be used to estimate variance components for some stochastic models of routine measurement systems under some conditions, because the likelihood function is unbounded for such stochastic models. No optimal solution of variance components exists for these likelihood functions from the point of view of global optimization, implying that variance components for such stochastic models of practical importance cannot be estimated by maximizing the likelihood function.
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Data Availability Statement
No data, models, or code were generated or used during the study.
Acknowledgments
The authors thank the handling editor and the anonymous reviewers for the constructive comments, which helped clarify some questions of concern. This work is partially supported by the National Natural Science Foundation of China (Nos. 41874012 and 41674013).
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Published In
Journal of Surveying Engineering
Volume 146 • Issue 2 • May 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Mar 17, 2019
Accepted: Oct 1, 2019
Published online: Feb 19, 2020
Published in print: May 1, 2020
Discussion open until: Jul 19, 2020
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