Journal article
Estimating high‐dimensional additive Cox model with time‐dependent covariate processes
Scandinavian journal of statistics, Vol.45(4), pp.900-922
12/2018
DOI: 10.1111/sjos.12327
Abstract
This paper is concerned with the estimation in the additive Cox model with time-dependent covariates when the number of additive components p is greater than the sample size n. By combining spline representation and the group lasso penalty, a penalized partial likelihood approach to estimating the unknown component functions is proposed. Given the non-iid nature of the log partial likelihood function and the nonparametric complexities of the component function estimation, it is challenging to analyze the theoretical properties of the proposed estimation. Through concentration inequities developed for martingale differences in the context of the additive Cox model, we establish nonasymptotic oracle inequalities for the group lasso in the additive Cox model with p=eo(n) under the compatibility and cone invertibility factors conditions on the Hessian matrix. An interesting and surprising aspect of our result is that the complexity of the component functions affects not only the approximation error but also the stochastic error. This is quite different from the additive mean models and suggests that the additive Cox model is more difficult to estimate than the additive mean models in high-dimensional settings.
Details
- Title: Subtitle
- Estimating high‐dimensional additive Cox model with time‐dependent covariate processes
- Creators
- Shaogao Lv - Southwestern University of Finance and EconomicsJiakun Jiang - Southwestern University of Finance and EconomicsFanyin Zhou - Southwestern University of Finance and EconomicsJian Huang - University of IowaHuazhen Lin - Southwestern University of Finance and Economics
- Resource Type
- Journal article
- Publication Details
- Scandinavian journal of statistics, Vol.45(4), pp.900-922
- DOI
- 10.1111/sjos.12327
- ISSN
- 0303-6898
- eISSN
- 1467-9469
- Grant note
- DOI: 10.13039/501100001809, name: National Natural Science Foundation of China, award: 11571282, 11528102; DOI: 10.13039/501100001809, name: National Natural Science Foundation of China, award: 11501463
- Language
- English
- Date published
- 12/2018
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9984257619602771
Metrics
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