Structured Estimation in Nonparameteric Cox Model
This work addresses structured estimation challenges in survival analysis for high-dimensional genetic data, representing an incremental advancement with specific theoretical extensions.
The paper tackles the problem of variable selection and estimation in high-dimensional nonparametric Cox proportional hazards models with censored data, developing novel non-asymptotic bounds and extending LAN principles to high-dimensional settings, showing that penalized estimators achieve finite-sample prediction properties comparable to those in linear models.
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.