caa a22 4500 475826922 CHVBK 20180406123831.0 cr unu---uuuuu 170329e20000601xx s 000 0 eng 10.1023/A:1004165822461 doi (NATIONALLICENCE)springer-10.1023/A:1004165822461 Bühlmann Peter Seminar für Statistik, ETH Zentrum, CH-8092, Zürich, Switzerland aut Model Selection for Variable Length Markov Chains and Tuning the Context Algorithm [Elektronische Daten] [Peter Bühlmann] We consider the model selection problem in the class of stationary variable length Markov chains (VLMC) on a finite space. The processes in this class are still Markovian of high order, but with memory of variable length. Various aims in selecting a VLMC can be formalized with different non-equivalent risks, such as final prediction error or expected Kullback-Leibler information. We consider the asymptotic behavior of different risk functions and show how they can be generally estimated with the same resampling strategy. Such estimated risks then yield new model selection criteria. In particular, we obtain a data-driven tuning of Rissanen's tree structured context algorithm which is a computationally feasible procedure for selection and estimation of a VLMC. The Institute of Statistical Mathematics, 2000 Bootstrap nationallicence zero-one loss nationallicence final prediction error nationallicence finite-memory source nationallicence FSMX model nationallicence Kullback-Leibler information nationallicence L 2 loss nationallicence optimal tree pruning nationallicence resampling nationallicence tree model nationallicence Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/2(2000-06-01), 287-315 0020-3157 52:2<287 2000 52 10463 https://doi.org/10.1023/A:1004165822461 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1004165822461 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Bühlmann Peter Seminar für Statistik, ETH Zentrum, CH-8092, Zürich, Switzerland aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/2(2000-06-01), 287-315 0020-3157 52:2<287 2000 52 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence SWISSBIB 142145246 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer