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Theory of Probability and Mathematical Statistics

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A comparative study for two newly developed estimators for the slope in the functional EIV linear model


Author: A. A. Al-Sharadqah
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 97 (2017).
Journal: Theor. Probability and Math. Statist. 97 (2018), 211-236
MSC (2010): Primary 68T10, 68K45, 68K40, 62P30
DOI: https://doi.org/10.1090/tpms/1058
Published electronically: February 21, 2019
MathSciNet review: 3746009
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Abstract: Two estimators were recently developed for the slope of a line in the functional EIV model. Both are unbiased, up to order $ \sigma ^4$, where $ \sigma $ is the error standard deviation. One estimator was constructed as a function of the maximum likelihood estimator (MLE). Therefore, it was called the Adjusted MLE (AMLE). The second estimator was constructed using a completely different approach. Although both the estimators are unbiased, up to the order $ \sigma ^4$, the latter estimator is much more accurate than the AMLE. We study these two estimators more rigorously here, and we show why one estimator outperforms the other one.


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Additional Information

A. A. Al-Sharadqah
Affiliation: Department of Mathematics and Interdisciplinary Research Institute for the Sciences, California State University-Northridge, Northridge, California 91330-8313
Email: ali.alsharadqah@csun.edu

DOI: https://doi.org/10.1090/tpms/1058
Keywords: Simple linear regression, errors-in-variables models, small-noise model, maximum likelihood estimator, bias correction, mean squared errors
Received by editor(s): May 3, 2017
Published electronically: February 21, 2019
Article copyright: © Copyright 2019 American Mathematical Society