Debiased calibration estimation using generalized entropy under selection bias
Date
2024-05
Authors
Kwon, Yonghyun
Major Professor
Advisor
Kim, Jae Kwang
Fuller, Wayne A
Yu, Cindy L
Zhu, Zhengyuan
Qiu, Yumou
Committee Member
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Altmetrics
Abstract
This dissertation addresses various topics in survey sampling and missing data analysis with a particular emphasis on calibration weighting. It consists of four chapters. In Chapter 2, we develop inference for parameters of a two-level model matching the design hierarchy of a two-stage sample. We propose a new method for the analysis of two-level models based on a normal approximation to the estimated cluster effects and taking account of design weights. In Chapter 3, we present a frequentist approach using a graphical model and fractional imputation, which can handle missing data for multivariate categorical variables under the missing at random assumption. We adopt the idea of a random forest to fit multiple reduced models and then combine multiple models using model weights. The model weights are computed from double projection, where the observed likelihood is projected on the class of a graphical mixture model. In Chapter 4, in the context of survey sampling, we introduce a novel framework that uses generalized entropy as the objective function for optimization, where design weights play a role in the constraints to ensure design consistency rather than being part of the objective function. This calibration framework is particularly attractive due to its generality and its ability to generate more efficient calibration weights compared to traditional methods based on divergences. In Chapter 5, in the context of missing data analysis, we introduce a class of calibration methods that employ generalized entropy to achieve double robustness and improve efficiency, even in cases of model misspecification. The proposed entropy calibration improves the efficiency of the classical empirical likelihood estimators while maintaining double robustness by altering the calibration constraint used in the empirical likelihood.
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Type
dissertation