Contributions to Penalized Estimation
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Shin, Sunyoung. Contributions to Penalized Estimation. Chapel Hill, NC: University of North Carolina at Chapel Hill Graduate School, 2014. https://doi.org/10.17615/6y8w-ng22APA
Shin, S. (2014). Contributions to Penalized Estimation. Chapel Hill, NC: University of North Carolina at Chapel Hill Graduate School. https://doi.org/10.17615/6y8w-ng22Chicago
Shin, Sunyoung. 2014. Contributions to Penalized Estimation. Chapel Hill, NC: University of North Carolina at Chapel Hill Graduate School. https://doi.org/10.17615/6y8w-ng22- Last Modified
- March 19, 2019
- Creator
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Shin, Sunyoung
- Affiliation: College of Arts and Sciences, Department of Statistics and Operations Research
- Abstract
- Penalized estimation is a useful statistical technique to prevent overfitting problems. In penalized methods, the common objective function is in the form of a loss function for goodness of fit plus a penalty function for complexity control. In this dissertation, we develop several new penalization approaches for various statistical models. These methods aim for effective model selection and accurate parameter estimation. The first part introduces the notion of partially overlapping models across multiple regression models on the same dataset. Such underlying models have at least one overlapping structure sharing the same parameter value. To recover the sparse and overlapping structure, we develop adaptive composite M-estimation (ACME) by doubly penalizing a composite loss function, as a weighted linear combination of the loss functions. ACME automatically circumvents the model misspecification issues inherent in other composite-loss-based estimators. The second part proposes a new refit method and its applications in the regression setting through model combination: ensemble variable selection (EVS) and ensemble variable selection and estimation (EVE). The refit method estimates the regression parameters restricted to the selected covariates by a penalization method. EVS combines model selection decisions from multiple penalization methods and selects the optimal model via the refit and a model selection criterion. EVE considers a factorizable likelihood-based model whose full likelihood is the multiplication of likelihood factors. EVE is shown to have asymptotic efficiency and computational efficiency. The third part studies a sparse undirected Gaussian graphical model (GGM) to explain conditional dependence patterns among variables. The edge set consists of conditionally dependent variable pairs and corresponds to nonzero elements of the inverse covariance matrix under the Gaussian assumption. We propose a consistent validation method for edge selection (CoVES) in the penalization framework. CoVES selects candidate edge sets along the solution path and finds the optimal set via repeated subsampling. CoVES requires simple computation and delivers excellent performance in our numerical studies.
- Date of publication
- August 2014
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- In Copyright
- Advisor
- Marron, James Stephen
- Liu, Yufeng
- Fine, Jason
- Zhang, Kai
- Kosorok, Michael
- Degree
- Doctor of Philosophy
- Degree granting institution
- University of North Carolina at Chapel Hill Graduate School
- Graduation year
- 2014
- Language
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- Place of publication
- Chapel Hill, NC
- Access right
- This item is restricted from public view for 1 year after publication.
- Date uploaded
- April 23, 2015
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