Estimating the inter-arrival time density of Markov renewal processes under structural assumptions on the transition distribution |
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| Authors: | Priscilla E. Greenwood Wolfgang Wefelmeyer |
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| Affiliation: | a Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada V6T 1Z2b Department of Mathematical Sciences, Binghamton University, Binghamton, NY 13902-6000, USAc Mathematical Institute, University of Cologne, 50931 Cologne, Germany |
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| Abstract: | We consider a stationary Markov renewal process whose inter-arrival time density depends multiplicatively on the distance between the past and present state of the embedded chain. This is appropriate when the jump size is governed by influences that accumulate over time. Then we can construct an estimator for the inter-arrival time density that has the parametric rate of convergence. The estimator is a local von Mises statistic. The result carries over to the corresponding semi-Markov process. |
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| Keywords: | primary, 62G07, 62M05 secondary, 62G20 |
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