A Sufficiency Property Arising from the Characterization of Extremes of Markov Chains
At extreme levels, it is known that for a particular choice of marginal distribution, transitions of a Markov chain behave like a random walk. For a broad class of Markov chains, we give a characterization for the step length density of the limiting random walk, which leads to an interesting suffici...
| Veröffentlicht in: | Bernoulli. - International Statistical Institute and Bernoulli Society for Mathematical Statistics and Probability, 1995. - 6(2000), 1, Seite 183-190 |
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| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2000
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| Zugriff auf das übergeordnete Werk: | Bernoulli |
| Schlagworte: | Extreme value theory Kernel density estimation Markov chain Random walk Sufficient statistics Mathematics Physical sciences Business Applied sciences Behavioral sciences |
| Zusammenfassung: | At extreme levels, it is known that for a particular choice of marginal distribution, transitions of a Markov chain behave like a random walk. For a broad class of Markov chains, we give a characterization for the step length density of the limiting random walk, which leads to an interesting sufficiency property. This representation also leads us to propose a new technique for kernel density estimation for this class of models. |
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| ISSN: | 13507265 |
| DOI: | 10.2307/3318638 |