Structured Estimation in Nonparameteric Cox Model

TL;DR

This paper develops finite sample properties and non-asymptotic bounds for structured estimation in high-dimensional nonparametric Cox models, addressing sparsity and censoring with novel penalties.

Contribution

It introduces a general class of group penalties for sparse structured variable selection and extends non-asymptotic LAN principles to high-dimensional Cox models.

Findings

Finite sample prediction properties match those of linear models.

Novel non-asymptotic sandwich bounds for partial likelihood.

Extension of LAN to high-dimensional spaces with p >> n.

Abstract

To better understand the interplay of censoring and sparsity we develop finite sample properties of nonparametric Cox proportional hazard's model. Due to high impact of sequencing data, carrying genetic information of each individual, we work with over-parametrized problem and propose general class of group penalties suitable for sparse structured variable selection and estimation. Novel non-asymptotic sandwich bounds for the partial likelihood are developed. We establish how they extend notion of local asymptotic normality (LAN) of Le Cam's. Such non-asymptotic LAN principles are further extended to high dimensional spaces where $p \gg n$. Finite sample prediction properties of penalized estimator in non-parametric Cox proportional hazards model, under suitable censoring conditions, agree with those of penalized estimator in linear models.