Bootstrap maximum likelihood for quasi-stationary distributions |
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Authors: | Guangbao Guo James Allison |
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Institution: | 1. School of Mathematics and Statistics, Shandong University of Technology, Zibo, People's Republic of China;2. Unit for Business Mathematics and Information, North-West University, Potchefstroom, South Africa |
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Abstract: | Quasi-stationary distributions have many applications in diverse research fields. We develop a bootstrap-based maximum likelihood (BML) method to deal with quasi-stationary distributions in statistical inference. To efficiently implement a bootstrap procedure that can handle the dependence among observations and speed up the computation, a novel block bootstrap algorithm is proposed to accommodate parallel bootstrap. In particular, we select a suitable block length for use with the parallel bootstrap. The estimation error is investigated to show its convergence. The proposed BML is shown to be asymptotically unbiased. Some numerical studies are given to examine the performance of the new algorithm. The advantages are evidenced through a comparison with some competitors and some examples are analysed for illustration. |
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Keywords: | Block bootstrap Markov processes maximum likelihood parallel bootstrap portfolio processes quasi-stationary distributions |
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