Cornelis J Potgieter, Michael C Byrd
Measurement error in observations is widely known to cause bias and a loss of power when fitting statistical models, particularly when studying distribution shape or the relationship between an outcome and a variable of interest. Most existing correction methods in the literature require strong assumptions about the distribution of the measurement error, or rely on ancillary data which is not always available. This limits the applicability of these methods in many situations. Furthermore, new correction approaches are also needed for high-dimensional settings, where the presence of measurement error in the covariates adds another level of complexity to the desirable structure of the models, such as sparsity. This dissertation presents new correction methods for measurement error in two important statistical problems: density deconvolution and errors-in-variables models.
For both density deconvolution and linear errors-in-variables regression, new estimators based on the empirical phase function are proposed. Compared to the existing methods, phase function-based estimators require only mild assumptions about the measurement error distribution. For high-dimensional errors-in-variables models, a new estimator that extends the flexible Simulation-Extrapolation (SIMEX) correction procedure is proposed in order to achieve sparsity of the solution. All the new estimators have been shown to have strong theoretical support and good finite sample performance. Data examples are provided to illustrate the practical use of each estimator in reality.
Cornelis J Potgieter
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