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theses

This dissertation develops methodologies for analysis of big data and its related theoretical properties. Recent years, tremendous progress has been made in analysis of big data, especially techniques via penalization and shrinkages. However, there are still many challenging problems to be solved. This dissertation focuses on two settings where (i) the data is too large to fit into a single computer or too expensive to perform a computationally intensive data analysis; or (ii) there are unknown group structures of highly correlated variables. In this dissertation, we first propose a Split-and-Conquer approach to analyze extraordinarily large data. Then, under linear regression settings with highly correlated variables, we investigate model selection properties of OSCAR (octagonal shrinkage and clustering algorithm for regression) estimators (Bondell & Reich, 2008) and propose a more general method Group OSCAR which incorporates both prior knowledge of group structures and correlation patterns among explanatory variables. We first propose a split-and-conquer approach and illustrate it using a computationally intensive penalized regression method. We show that the combined result is asymptotically equivalent to the corresponding analysis result of using the entire data all together. In addition, we demonstrate that the approach has an inherent advantage of being more resistant to false model selections. Furthermore, when a computational intensive algorithm is used, we show that the split-and-conquer approach can substantially reduce computing time and computer memory requirement. Detecting meaningful `groups' of highly correlated variables has been studied a lot. OSCAR estimators provide a feasible way to perform variable selection and clustering simultaneously. However, no theoretical results are provided for OSCAR estimators. In this dissertation, we provide a set of mild conditions under which OSCAR estimators are able to select the true model and keep the order of the coefficients by their magnitudes when the correlations are high. In the last part of this dissertation, we propose a new method. This method not only takes use of known group structures but also incorporates the correlation patterns leading to the underlying unknown group structure. It extends most of the model selections methods in the literature, and has a general grouping effect.

ETD_4452

Ph.D.

Includes bibliographical references

Includes vita

by Xueying Chen

http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000067642

doi:10.7282/T37S7MGK

ETD doctoral

The author owns the copyright to this work.