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Title: Measurement error in linear regression models with fat tails and skewed errors Authors:  Mahmoud Torabi - University of Manitoba (Canada)
Malay Ghosh - University of Florida (United States)
Jiyoun Myung - California State University, East Bay (United States) [presenting]
Mark Steel - University of Warwick (United Kingdom)
Abstract: Linear regression models, which account for skewed error distributions with fat tails, have been previously studied and often observed in real data analyses. Covariates measured with 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 particulate matter, which is one of the most critical air pollutants and has a major impact on human health and the environment. However, the wind speed is measured with error, and the distribution of particulate matter is neither symmetric nor normally distributed. Ignoring the issue of measurement error in covariates may produce bias in model parameters estimate and lead to wrong conclusions. A hierarchical Bayesian approach is implemented for properly studying linear regression models where the covariates are measured with error and error distribution is skewed with fat tails. The performance of the proposed approach is evaluated through a simulation study and also by a real data application.