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-\(n\) consistent and the estimated functions achieving optimal convergence rates. Asymptotic normality is also established for the estimators.
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Acknowledgments
This work was partially supported by the National Natural Science Fund for Distinguished Young Scholar (No. 70825004), the National Natural Science Foundation of China (NSFC) (Nos. 10731010, 11301424 and 10628104), the National Basic Research Program (No. 2007CB814902), Creative Research Groups of China (No. 10721101), and Leading Academic Discipline Program, 211 Project for Shanghai University of Finance and Economics (the 3rd phase) (No. B803). The authors thank the editor, an associate editor and two referees for helpful comments and suggestions. The usual disclaimer applies.
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Ma, Y., Wan, A.T.K., Chen, X. et al. On estimation and inference in a partially linear hazard model with varying coefficients. Ann Inst Stat Math 66, 931–960 (2014). https://doi.org/10.1007/s10463-013-0430-0
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DOI: https://doi.org/10.1007/s10463-013-0430-0