Mathematical Sciences: Measurement Error and Statistical Inference

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This research develops new methods of statistical inference for data measured with error. The methods exploit the availability of high-speed computing to simulate the effects of measurement error on a data set. The results of such simulation experiments form the basis of a method of inference called simulation extrapolation. The first component of the research adapts the method of simulation extrapolation estimation to situations in which replicate measurements are made on the variables measured with error. The second component of the research uses the complex-variable formulation of simulation extrapolation to bypass the extrapolation step. This is accomplished by performing a simulation experiment using complex pseudo random variables to compute unbiased estimating equations for the parameters of interest. The third component of the research focuses on two-sample hypothesis testing problems, developing tests that are asymptotically valid when data from one sample are measured with error. The presence of measurement error in data can affect the validity of conclusions drawn from statistical analyses of such data. For example, measurement error in risk factors such as blood pressure or cholesterol level affects statistical determination of the relationship of heart disease to such risk factors, usually resulting in underestimation of the beneficial effects of controlling these risk factors. Similarly, statistical determination of the relationship of ecosystem health to ecosystem stressers (pollutants, for example) can be obscured by the inability to accurately measure stresser levels. This research develops statistical theory and methods for making valid inferences from data that are measured with error. The fact that errors of measurement occur in many areas of science (survey methodology, environmental studies, epidemiology, medicine for example) means that the research is widely applicable. The research uses novel computer simulation methods to simulate the effects of measurement error on a data set and on the conclusions drawn from such data. The information obtained from the simulation studies is then used to make valid inferences from the data that are free from the biasing effects of measurement error.