Doctor of Philosophy (Ph.D.), Bowling Green State University, 2015, Statistics

The performances of penalized least squares approaches profoundly depend on the selection of the tuning parameter; however, statisticians did not reach consensus on the criterion for choosing the tuning parameter. Moreover, the penalized least squares estimation that based on a single value of the tuning parameter suffers from several drawbacks. The tuning parameter selected by the traditional selection criteria such as AIC, BIC, CV tends to pick excessive variables, which results in an over-fitting model. On the contrary, many other criteria, such as the extended BIC that favors an over-sparse model, may run the risk of dropping some relevant variables in the model. In the dissertation, a novel approach for the feature selection based on the whole solution paths is proposed, which significantly improves the selection accuracy. The key idea is to partition the variables into the relevant set and the irrelevant set at each tuning parameter, and then select the variables which have been classified as relevant for at least one tuning parameter. The approach is named as Selection by Partitioning the Solution Paths (SPSP). Compared with other existing feature selection approaches, the proposed SPSP algorithm allows feature selection by using a wide class of penalty functions, including Lasso, ridge and other strictly convex penalties. Based on the proposed SPSP procedure, a new type of scores are presented to rank the importance of the variables in the model. The scores, noted as Area-out-of-zero-region Importance Scores (AIS), are defined by the areas between the solution paths and the boundary of the partitions over the whole solution paths. By applying the proposed scores in the stepwise selection, the false positive error of the selection is remarkably reduced. The asymptotic properties for the proposed SPSP estimator have been well established. It is showed that the SPSP estimator is selection consistent when the original estimator is either estimation con (open full item for complete abstract)

Committee: Hanfeng Chen (Committee Chair); Peng Wang (Advisor); James Albert (Committee Member); Jonathan Bostic (Other) Subjects: Statistics