Statistical Topics and Stochastic Models for Dependent Data with Applications E-Book
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- Herausgeber: John Wiley & Sons
- Kategorie: Bildung
- Sprache: Englisch
This book is a collective volume authored by leading scientists in the field of stochastic modelling, associated statistical topics and corresponding applications. The main classes of stochastic processes for dependent data investigated throughout this book are Markov, semi-Markov, autoregressive and piecewise deterministic Markov models. The material is divided into three parts corresponding to: (i) Markov and semi-Markov processes, (ii) autoregressive processes and (iii) techniques based on divergence measures and entropies. A special attention is payed to applications in reliability, survival analysis and related fields.
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Seitenzahl: 410
Veröffentlichungsjahr: 2020
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Table of Contents
Cover
Title page
Copyright
Preface
PART 1: Markov and Semi-Markov Processes
1 Variable Length Markov Chains, Persistent Random Walks: A Close Encounter
1.1. Introduction
1.2. VLMCs: definition of the model
1.3. Definition and behavior of PRWs
1.4. VLMC: existence of stationary probability measures
1.5. Where VLMC and PRW meet
1.6. References
2 Bootstraps of Martingale-difference Arrays Under the Uniformly Integrable Entropy
2.1. Introduction and motivation
2.2. Some preliminaries and notation
2.3. Main results
2.4. Application for the semi-Markov kernel estimators
2.5. Proofs
2.6. References
3 A Review of the Dividend Discount Model: From Deterministic to Stochastic Models
3.1. Introduction
3.2. General model
3.3. Gordon growth model and extensions
3.4. Markov chain stock models
3.5. Conclusion
3.6. References
4 Estimation of Piecewise-deterministic Trajectories in a Quantum Optics Scenario
4.1. Introduction
4.2. Problem formulation
4.3. Estimation procedure
4.4. Physical interpretation
4.5. Concluding remarks
4.6. References
5 Identification of Patterns in a Semi-Markov Chain
5.1. Introduction
5.2. The prefix chain
5.3. The semi-Markov setting
5.4. The hitting time of the pattern
5.5. A genomic application
5.6. Concluding remarks
5.7. References
PART 2: Autoregressive Processes
6 Time Changes and Stationarity Issues for Continuous Time Autoregressive Processes of Order
p
6.1. Introduction
6.2. Basics
6.3. Stationary AR processes
6.4. Time transforms
6.5. Conclusion
6.6. Appendix
6.7. References
7 Sequential Estimation for Non-parametric Autoregressive Models
7.1. Introduction
7.2. Main conditions
7.3. Pointwise estimation with absolute error risk
7.4. Estimation with quadratic integral risk
7.5. References
PART 3: Divergence Measures and Entropies
8 Inference in Parametric and Semi-parametric Models: The Divergence-based Approach
8.1. Introduction
8.2. Models and selection of statistical criteria
8.3. Non-regular cases: the interplay between the model and the criterion
8.4. References
9 Dynamics of the Group Entropy Maximization Processes and of the Relative Entropy Group Minimization Processes Based on the Speed-gradient Principle
9.1. Introduction
9.2. Group entropies and the SG principle
9.3. Relative entropy group and the SG principle
9.4. A new (
G, a
) power relative entropy group and the SG principle
9.5. Conclusion
9.6. References
10 Inferential Statistics Based on Measures of Information and Divergence
10.1. Introduction
10.2. Divergence measures
10.3. Properties of divergence measures
10.4. Model selection criteria
10.5. Goodness of fit tests
10.6. Simulation study
10.7. References
11 Goodness-of-Fit Tests Based on Divergence Measures for Frailty Models
11.1. Introduction
11.2. The proposed goodness-of-fit test
11.3. Main results
11.4. Frailty models
11.5. Simulations
11.6. References
List of Authors
Index
End User License Agreement
Guide
Cover
Table of Contents
Title page
Copyright
Preface
Begin Reading
List of Authors
Index
End User License Agreement
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Series EditorNikolaos Limnios
Statistical Topics and Stochastic Models for Dependent Data with Applications
Edited byVlad Stefan BarbuNicolas Vergne
First published 2020 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:
ISTE Ltd John27-37 St George’s RoadLondon SW19 4EUUKwww.iste.co.uk
Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USAwww.wiley.com
© ISTE Ltd 2020
The rights of Vlad Stefan Barbu and Nicolas Vergne to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.
Library of Congress Control Number: 2020938718
British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-78630-603-6
Preface
This collective book stems from a workshop that took place in Rouen, October 3–5, 2018, within the framework of the project Random Models and Statistical Tools, Informatics and Combinatorics (MOUSTIC – Modèles aléatoires et Outils Statistiques, Informatiques et Combinatoires), financed by the Region of Normandy and the European Regional Development Fund. The main idea was to bring together leading scientists working on probabilistic and statistical topics for dependent data, as well as on associated applications.
This is the way this book was written, with the intention to offer to the scientific community a part of the latest advances in the field of stochastic modeling for dependent data, authored by leading experts in the field. This is a crucial aspect in a time when we face an increasing need for more and more complex models capable of capturing the main features of increasingly complex applications. From a technical point of view, our book is important for gathering theoretical developments and applications related to Markov type models (semi-Markov processes, autoregressive processes, piecewise deterministic Markov processes, and variable length Markov chains) as well as probabilistic/statistical techniques issued from information theory, based on divergence measures and entropies.
This volume is divided into three parts: the first one examines Markov and semi-Markov processes, the second one deals with autoregressive processes and the last one presents divergence measures and entropies. Particular attention is given to applications of these methods in various fields such as finance, DNA analysis, quantum physics and survival analysis.
The workshop in Rouen and, consequently, the present book, would not have been possible without the support of the Laboratory of Mathematics Raphaël Salem, the Laboratory of Mathematics Nicolas Oresme, the University of Rouen Normandy, the Region of Normandy, the French Statistical Society-SFdS, the MAS group of the French Society of Applied and Industrial Mathematics-SMAI, the Normandie-Mathématiques Research Federation and the Normastic Research Federation.
We would like to thank all the speakers of the workshop who contributed, although some of them indirectly, to the quality of the present volume. Our thanks go also to the anonymous reviewers for their valuable work: without their support, this volume could not have been successfully completed.
We would also like to thank Professor Nikolaos Limnios for proposing and encouraging us to elaborate this collective volume as well as the editorial staff of ISTE Ltd for their technical support.
Vlad Stefan BARBU
Nicolas VERGNE
Rouen, May 2020
