Mathematical Sciences: Statistical Theory and Procedures forErrors in Variables Regression and Related Reliability

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Ignoring the errors in the explanatory variables, as in classical least squares, can introduce serious bias in the fitted function. This research will incorporate partial information from various sources using either Bayesian or frequentist techniques or combinations, will evaluate the resultant methodologies, and will apply these methods to measurement error problems arising in chemistry and environmental monitoring. Regression models describe relationships among explanatory and response variables. When the explanatory variables are also subject to random error, the regression model may be systematically distorted unless special analyses are used. This research will extend these special analyses to incorporate information about the reliability of the explanatory variables. The new methods for analysis should find application in chemistry and environmental monitoring (to be tried as part of this research), astronomy, medicine and behavioral science.