Structured Estimation in Nonparameteric Cox Model

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.

References in corpus (9)

• The composite absolute penalties family for grouped and hierarchical variable selection
• Component selection and smoothing in multivariate nonparametric regression
• Lasso-type recovery of sparse representations for high-dimensional data
• High-dimensional generalized linear models and the lasso
• Sparsity oracle inequalities for the Lasso
• Aggregation for Gaussian regression
• Regularization for Cox's proportional hazards model with NP-dimensionality
• Oracle inequalities for the lasso in the Cox model
• Kullback-Leibler aggregation and misspecified generalized linear models

Cited by in corpus (1)

• Fine-Gray competing risks model with high-dimensional covariates: estimation and Inference