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0Dissertation - Model Robust Regression Based on...

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Unformatted text preview: Model Robust Regression Based on Generalized Estimating Equations by Seth K. Clark Dissertation submitted to the faculty of Virginia Polytechnic Institute and State University in partial fulllment of the requirements for the degree of Doctor of Philosophy in Statistics Jerey B. Birch, Co-Chairman Oliver Schabenberger, Co-Chairman George R. Terrell Keying Ye Christine M. Anderson-Cook March 29, 2002 Blacksburg, VA Keywords: Model Misspecication, Semiparametric, Nonparametric Regression, Local Model Copyright 2002, Seth K. Clark Model Robust Regression Based on Generalized Estimating Equations by Seth K. Clark Jerey B. Birch and Oliver Schabenberger, Chairmen Statistics Abstract One form of model robust regression (MRR) predicts mean response as a convex combi-nation of a parametric and a nonparametric prediction. MRR is a semiparametric method by which an incompletely or an incorrectly specied parametric model can be improved through adding an appropriate amount of a nonparametric t. The combined predictor can have less bias than the parametric model estimate alone and less variance than the nonparametric esti-mate alone. Additionally, as shown in previous work for uncorrelated data with linear mean function, MRR can converge faster than the nonparametric predictor alone. We extend the MRR technique to the problem of predicting mean response for clustered non-normal data. We combine a nonparametric method based on local estimation with a global, parametric generalized estimating equations (GEE) estimate through a mixing parameter on both the mean scale and the linear predictor scale. As a special case, when data are uncorrelated, this amounts to mixing a local likelihood estimate with predictions from a global general-ized linear model. Cross-validation bandwidth and optimal mixing parameter selectors are developed. The global ts and the optimal and data-driven local and mixed ts are studied under no/some/substantial model misspecication via simulation. The methods are then illustrated through application to data from a longitudinal study. Acknowledgements Completion of this degree would not have been possible without the continuous support from my advisors Jerey Birch and Oliver Schabenberger. I am very fortunate to have had the opportunity to work with them. They invested hundreds of hours to support me in this research, provided invaluable guidance, were patient, and took interest in my well-being. They listened to my talks, read and corrected several drafts, and always made themselves available whenever possible. I thank Dr. Birch especially for bringing my attention to his workcombining parametric and nonparametric regressionI have found it to be a fascinating area. I thank Dr. Schabenberger especially for his expertise with correlated data, the context of my research. Special thanks are in order for my other committee members: George Terrell, Christine Anderson-Cook, and Keying Ye. I appreciate their taking an interest in my research. I thank Dr. Terrell for understanding my change in taking an interest in my research....
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This note was uploaded on 11/08/2009 for the course STATS 241 taught by Professor Lai,t during the Spring '08 term at Stanford.

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0Dissertation - Model Robust Regression Based on...

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