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Abstract: Suppose we observe a geometrically ergodic semi-Markov process and have aparametric model for the transition distribution of the embedded Markov chain,for the conditional distribution of the inter-arrival times, or for both. Thefirst two models for the process are semiparametric, and the parameters can beestimated by conditional maximum likelihood estimators. The third model for theprocess is parametric, and the parameter can be estimated by an unconditionalmaximum likelihood estimator. We determine heuristically the asymptoticdistributions of these estimators and show that they are asymptoticallyefficient. If the parametric models are not correct, the conditional maximumlikelihood estimators estimate the parameter that maximizes theKullback-Leibler information. We show that they remain asymptoticallyefficient in a nonparametric sense.



Author: Ursula U. Müller, Anton Schick, Wolfgang Wefelmeyer

Source: https://arxiv.org/







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