Non-asymptotic oracle inequalities for the high-dimensional cox regression via lasso release_6hdikuvvsvebpfi2ojwinp3a3e

by Shengchun Kong, Bin Nan

Published in Statistica sinica by Institute of Statistical Science.

2013   Volume 24, Issue 1, p25-42

Abstract

We consider finite sample properties of the regularized high-dimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. The summands in the negative log partial likelihood function for censored survival data, however, are neither iid nor Lipschitz.We first approximate the negative log partial likelihood function by a sum of iid non-Lipschitz terms, then derive the non-asymptotic oracle inequalities for the lasso penalized Cox regression using pointwise arguments to tackle the difficulties caused by lacking iid Lipschitz losses.
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Type  article-journal
Stage   published
Date   2014-01-01
Language   en ?
DOI  10.5705/ss.2012.240
PubMed  24516328
PMC  PMC3916829
Wikidata  Q29011590
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