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Measurement error in linear regression models with fat tails and skewed errors
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Torabi, Mahmoud, Ghosh, Malay, Myung, Jiyoun and Steel, Mark F. J. (2023) Measurement error in linear regression models with fat tails and skewed errors. Communications in Statistics - Theory and Methods, 52 (15). 5407-5426 . doi:10.1080/03610926.2021.2008442 ISSN 0361-0926.
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WRAP-Measurement-error-linear-regression-models-fat-tails-skewed-errors-2021.pdf - Accepted Version - Requires a PDF viewer. Download (672Kb) | Preview |
Official URL: http://dx.doi.org/10.1080/03610926.2021.2008442
Abstract
Linear regression models which account for skewed error distributions with fat tails have been previously studied. These two important features, skewness, and fat tails, are often observed in real data analyses. Covariates measured with an error also happen frequently in the observational data set-up. As a motivating example, wind speed as a covariate is usually used, among other covariates, to estimate the particulate matter (PM) which is one of the most critical air pollutants and has a major impact on human health and on the environment. However, the wind speed is measured with error and the distribution of PM is neither symmetric nor normally distributed (see Section “PM data application in Canada” for more details). Ignoring the issue of measurement error in covariates may produce bias in model parameters estimate and lead to wrong conclusions. In this paper, we propose an approach to study properly linear regression models where the covariates are measured with error and the error distribution is skewed with fat tails. We use a hierarchical Bayesian approach for inference, addressing also sensitivity of the results to priors. Performance of the proposed approach is evaluated through a simulation study and also by a real data application (PM in Canada).
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Library of Congress Subject Headings (LCSH): | Bayesian statistical decision theory, Regression analysis, Skew fields , Distribution (Probability theory), Analysis of covariance | ||||||||
Journal or Publication Title: | Communications in Statistics - Theory and Methods | ||||||||
Publisher: | Routledge | ||||||||
ISSN: | 0361-0926 | ||||||||
Official Date: | 2023 | ||||||||
Dates: |
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Volume: | 52 | ||||||||
Number: | 15 | ||||||||
Page Range: | 5407-5426 | ||||||||
DOI: | 10.1080/03610926.2021.2008442 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 19 January 2022 | ||||||||
Date of first compliant Open Access: | 26 November 2022 | ||||||||
RIOXX Funder/Project Grant: |
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