Nonparametric Learning in Hazard Regression

• Activity Number: 509
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Jelena Bradic*+
• Companies: University of California at San Diego
• Keywords: oracle inequalities ; group lasso ; partiali-likelihood ; censored data

Abstract

In this paper we introduce a framework to work under hazard regression models with nonparametric structure in high dimensions. For broad penalty structures that accomodate non-parametric setup, we extend LeCam's Local Asymptotic Normality approach to non-asymptotic setting. Using non-asymptotic quadratic bounds for log partial likelihood we prove finite sample risk properties for penalized estimators that hold true even for $p\gg n$ and of the order of $e^n$ by first localizing estimator to small neighborhoods. To the besto of our knowledge, oracle Inequalities of this kind have not been discussed before in the literature.