Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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ALMOST SURE LIMITS OF SAMPLE ALIGNMENTS IN PROPORTIONAL HAZARDS MODELS

  • Lim Jo-Han (Department of Applied Statistics, Yonsei University) ;
  • Kim Seung-Jean (Department of Electrical Engineering, Stanford University)
  • Published : 2006.09.01
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Abstract

The proportional hazards model (PHM) can be associated with a non- homogeneous Markov chain (NHMC) in the sense that sample alignments in the PHM correspond to trajectories of the NHMC. As a result the partial likelihood widely used for the PHM is a probabilistic function of the trajectories of the NHMC. In this paper, we show that, as the total number of subjects involved increases, the trajectories of the NHMC, i.e. sample alignments in the PHM, converges to the solution of an ordinary differential equation which, subsequently, characterizes the almost sure limit of the partial likelihood.

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References

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