Smoothed nonparametric estimation in window censored semi-Markov processes |
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| Institution: | 1. IGPM, RWTH Aachen, 52056 Aachen, Germany;2. Karlsruhe Institute of Technology, Steinbuch Center for Computing, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany;3. Im Hainzenthal 27, 67722 Winnweiler, Germany;1. School of Mathematics, Hefei University of Technology, Hefei, 230009, PR China;2. Institut de Mathématiques, Université Paul Sabatier, Toulouse, France;1. LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, China;2. Department of Mathematics, Southern Methodist University, Dallas, TX 75275, USA |
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| Abstract: | Consider a process that jumps among a finite set of states, with random times spent in between. In semi-Markov processes transitions follow a Markov chain and the sojourn distributions depend only on the connecting states. Suppose that the process started far in the past, achieving stationary. We consider non-parametric estimation by modelling the log-hazard of the sojourn times through linear splines; and we obtain maximum penalized likelihood estimators when data consist of several i.i.d. windows. We prove consistency using Grenander's method of sieves. |
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