Nonparametric Shrinkage Estimation for Aalen's Additive Hazards Model
Version of Record online: 7 APR 2014
© 2014 Australian Statistical Publishing Association Inc. Published by Wiley Publishing Asia Pty Ltd.
Australian & New Zealand Journal of Statistics
Volume 56, Issue 1, pages 15–26, March 2014
How to Cite
Hussein, A. A., Nkurunziza, S. and Tomanelli, K. (2014), Nonparametric Shrinkage Estimation for Aalen's Additive Hazards Model. Australian & New Zealand Journal of Statistics, 56: 15–26. doi: 10.1111/anzs.12067
- Issue online: 17 APR 2014
- Version of Record online: 7 APR 2014
- NSERC Canada Discovery grants
- integrated mean squared error;
- James-Stein estimator;
- ridge regression
Aalen's nonparametric additive model in which the regression coefficients are assumed to be unspecified functions of time is a flexible alternative to Cox's proportional hazards model when the proportionality assumption is in doubt. In this paper, we incorporate a general linear hypothesis into the estimation of the time-varying regression coefficients. We combine unrestricted least squares estimators and estimators that are restricted by the linear hypothesis and produce James-Stein-type shrinkage estimators of the regression coefficients. We develop the asymptotic joint distribution of such restricted and unrestricted estimators and use this to study the relative performance of the proposed estimators via their integrated asymptotic distributional risks. We conduct Monte Carlo simulations to examine the relative performance of the estimators in terms of their integrated mean square errors. We also compare the performance of the proposed estimators with a recently devised LASSO estimator as well as with ridge-type estimators both via simulations and data on the survival of primary billiary cirhosis patients.