Date Available
9-3-2016
Year of Publication
2015
Document Type
Doctoral Dissertation
Degree Name
Doctor of Philosophy (PhD)
College
Arts and Sciences
Department/School/Program
Statistics
Advisor
Dr. David M. Allen
Co-Director of Graduate Studies
Dr. Constance L. Wood
Abstract
Here we consider penalized regression methods, and extend on the results surrounding the l1 norm penalty. We address a more recent development that generalizes previous methods by penalizing a linear transformation of the coefficients of interest instead of penalizing just the coefficients themselves. We introduce an approximate algorithm to fit this generalization and a fully Bayesian hierarchical model that is a direct analogue of the frequentist version. A number of benefits are derived from the Bayesian persepective; most notably choice of the tuning parameter and natural means to estimate the variation of estimates – a notoriously difficult task for the frequentist formulation. We then introduce Bayesian trend filtering which exemplifies the benefits of our Bayesian version. Bayesian trend filtering is shown to be an empirically strong technique for fitting univariate, nonparametric regression. Through a simulation study, we show that Bayesian trend filtering reduces prediction error and attains more accurate coverage probabilities over the frequentist method. We then apply Bayesian trend filtering to real data sets, where our method is quite competitive against a number of other popular nonparametric methods.
Recommended Citation
Roualdes, Edward A., "New Results in ell_1 Penalized Regression" (2015). Theses and Dissertations--Statistics. 13.
https://uknowledge.uky.edu/statistics_etds/13
