Asymptotic normality for discretely observed Markov jump processes with an absorbing state |
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| Institution: | 1. 231 W. Hancock St, Campus Box 17, Department of Mathematics, Georgia College & State University, Milledgeville, GA 31061, United States;2. 221 Parker Hall, Department of Mathematics and Statistics, Auburn University, Auburn, Al 36849, United States;1. Department of Mathematics and Statistics, Concordia University, Montréal, QC H3G 1M8, Canada;2. Department of Mathematical Sciences, Central Connecticut State University, 1615 Stanley Street, New Britain, CT 06050, USA;1. University of St.Gallen, Bodanstrasse 6, 9000 St.Gallen, Switzerland;2. London School of Economics, Houghton Street, London WC2A 2AE, UK;1. Department of Economics, University of Chicago, 1126 East 59th Street, Chicago, IL 60637, United States;2. Department of Economics, University of Calgary, Calgary, Alberta T2N 1N4, Canada;1. Fachbereich Mathematik, Technische Universität Kaiserslautern, Erwin-Schrödinger Straße, 67653 Kaiserslautern, Germany;2. Fachgruppe Stochastik am Mathematischen Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Straße 4, 24098 Kiel, Germany;3. Department of Mathematics, SPST, University of Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany;4. School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland |
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| Abstract: | For a continuous-time Markov process, occasionally, only discrete-time observations are available. For a simple sample of homogeneous Markov jump processes with an absorbing state, observed each on a stochastic grid of time points, we establish asymptotic normality of the maximum likelihood estimator and close the gap in Kremer and Weißbach (2013). By showing that the solution of the Kolmogorov backward equation system is continuous differentiable, we can apply results for M-estimators. |
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| Keywords: | Multiple Markov jump process Discrete observations Asymptotic normality Parametric maximum likelihood |
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