Universal Coding and Order Identification by Model Selection Methods
The purpose of these notes is to highlight the far-reaching connections between Information Theory and Statistics. Universal coding and adaptive compression are indeed closely related to statistical inference concerning processes and using maximum likelih
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Élisabeth Gassiat
Universal Coding and Order Identification by Model Selection Methods
Springer Monographs in Mathematics Editors-in-Chief Isabelle Gallagher, Paris, France Minhyong Kim, Oxford, UK Series Editors Sheldon Axler, San Francisco, USA Mark Braverman, Princeton, USA Maria Chudnovsky, Princeton, USA Sinan C. Güntürk, New York, USA Tadahisa Funaki, Tokyo, Japan Claude Le Bris, Marne la Vallée, France Pascal Massart, Orsay, France Alberto Pinto, Porto, Portugal Gabriella Pinzari, Napoli, Italy Ken Ribet, Berkeley, USA René Schilling, Dresden, Germany Panagiotis Souganidis, Chicago, USA Endre Süli, Oxford, UK Shmuel Weinberger, Chicago, USA Boris Zilber, Oxford, UK
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Élisabeth Gassiat
Universal Coding and Order Identification by Model Selection Methods
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Élisabeth Gassiat Laboratoire de Mathématiques Université Paris-Sud Orsay Cedex, France Translated by Anna Ben-Hamou, LPSM, Sorbonne Université, Paris, France
ISSN 1439-7382 ISSN 2196-9922 (electronic) Springer Monographs in Mathematics ISBN 978-3-319-96261-0 ISBN 978-3-319-96262-7 (eBook) https://doi.org/10.1007/978-3-319-96262-7 Library of Congress Control Number: 2018948590 Mathematics Subject Classification (2010): 68P30, 62C10 Translation from the French language edition: Codage universel et identification d’ordre par sélection de modèles by Elisabeth Gassiat, © Société Mathématique de France 2014. All Rights Reserved. © Springer International Publishing AG, part of Springer Nature 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication.
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