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On estimation and inference in a partially linear hazard model with varying coefficients

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  • Yunbei Ma
  • Alan Wan
  • Xuerong Chen
  • Yong Zhou

Abstract

We study estimation and inference in a marginal proportional hazards model that can handle (1) linear effects, (2) non-linear effects and (3) interactions between covariates. The model under consideration is an amalgamation of three existing marginal proportional hazards models studied in the literature. Developing an estimation and inference procedure with desirable properties for the amalgamated model is rather challenging due to the co-existence of all three effects listed above. Much of the existing literature has avoided the problem by considering narrow versions of the model. The object of this paper is to show that an estimation and inference procedure that accommodates all three effects is within reach. We present a profile partial-likelihood approach for estimating the unknowns in the amalgamated model with the resultant estimators of the unknown parameters being root- $$n$$ n consistent and the estimated functions achieving optimal convergence rates. Asymptotic normality is also established for the estimators. Copyright The Institute of Statistical Mathematics, Tokyo 2014

Suggested Citation

  • Yunbei Ma & Alan Wan & Xuerong Chen & Yong Zhou, 2014. "On estimation and inference in a partially linear hazard model with varying coefficients," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(5), pages 931-960, October.
    • Handle: RePEc:spr:aistmt:v:66:y:2014:i:5:p:931-960
    DOI: 10.1007/s10463-013-0430-0
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    References listed on IDEAS

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    1. Jianwen Cai & Jianqing Fan & Jiancheng Jiang & Haibo Zhou, 2008. "Partially linear hazard regression with varying coefficients for multivariate survival data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 141-158, February.
    2. Lu Tian & David Zucker & L.J. Wei, 2005. "On the Cox Model With Time-Varying Regression Coefficients," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 172-183, March.
    3. Robinson, Peter M, 1988. "The Stochastic Difference between Econometric Statistics," Econometrica, Econometric Society, vol. 56(3), pages 531-548, May.
    4. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    5. Cai, Jianwen & Fan, Jianqing & Jiang, Jiancheng & Zhou, Haibo, 2007. "Partially Linear Hazard Regression for Multivariate Survival Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 538-551, June.
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