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Statistical Topics and Stochastic Models for Dependent Data with Applications

Release Date: 2020/12/01
ISBN: 9781786306036
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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.

Table of Contents

  1. Cover
  2. Title page
  3. Copyright
  4. Preface
  5. PART 1: Markov and Semi-Markov Processes
    1. 1 Variable Length Markov Chains, Persistent Random Walks: A Close Encounter
    2. 1.1. Introduction
    3. 1.2. VLMCs: definition of the model
    4. 1.3. Definition and behavior of PRWs
    5. 1.4. VLMC: existence of stationary probability measures
    6. 1.5. Where VLMC and PRW meet
    7. 1.6. References
    8. 2 Bootstraps of Martingale-difference Arrays Under the Uniformly Integrable Entropy
    9. 2.1. Introduction and motivation
    10. 2.2. Some preliminaries and notation
    11. 2.3. Main results
    12. 2.4. Application for the semi-Markov kernel estimators
    13. 2.5. Proofs
    14. 2.6. References
    15. 3 A Review of the Dividend Discount Model: From Deterministic to Stochastic Models
    16. 3.1. Introduction
    17. 3.2. General model
    18. 3.3. Gordon growth model and extensions
    19. 3.4. Markov chain stock models
    20. 3.5. Conclusion
    21. 3.6. References
    22. 4 Estimation of Piecewise-deterministic Trajectories in a Quantum Optics Scenario
    23. 4.1. Introduction
    24. 4.2. Problem formulation
    25. 4.3. Estimation procedure
    26. 4.4. Physical interpretation
    27. 4.5. Concluding remarks
    28. 4.6. References
    29. 5 Identification of Patterns in a Semi-Markov Chain
    30. 5.1. Introduction
    31. 5.2. The prefix chain
    32. 5.3. The semi-Markov setting
    33. 5.4. The hitting time of the pattern
    34. 5.5. A genomic application
    35. 5.6. Concluding remarks
    36. 5.7. References
  6. PART 2: Autoregressive Processes
    1. 6 Time Changes and Stationarity Issues for Continuous Time Autoregressive Processes of Order p
    2. 6.1. Introduction
    3. 6.2. Basics
    4. 6.3. Stationary AR processes
    5. 6.4. Time transforms
    6. 6.5. Conclusion
    7. 6.6. Appendix
    8. 6.7. References
    9. 7 Sequential Estimation for Non-parametric Autoregressive Models
    10. 7.1. Introduction
    11. 7.2. Main conditions
    12. 7.3. Pointwise estimation with absolute error risk
    13. 7.4. Estimation with quadratic integral risk
    14. 7.5. References
  7. PART 3: Divergence Measures and Entropies
    1. 8 Inference in Parametric and Semi-parametric Models: The Divergence-based Approach
    2. 8.1. Introduction
    3. 8.2. Models and selection of statistical criteria
    4. 8.3. Non-regular cases: the interplay between the model and the criterion
    5. 8.4. References
    6. 9 Dynamics of the Group Entropy Maximization Processes and of the Relative Entropy Group Minimization Processes Based on the Speed-gradient Principle
    7. 9.1. Introduction
    8. 9.2. Group entropies and the SG principle
    9. 9.3. Relative entropy group and the SG principle
    10. 9.4. A new (G, a) power relative entropy group and the SG principle
    11. 9.5. Conclusion
    12. 9.6. References
    13. 10 Inferential Statistics Based on Measures of Information and Divergence
    14. 10.1. Introduction
    15. 10.2. Divergence measures
    16. 10.3. Properties of divergence measures
    17. 10.4. Model selection criteria
    18. 10.5. Goodness of fit tests
    19. 10.6. Simulation study
    20. 10.7. References
    21. 11 Goodness-of-Fit Tests Based on Divergence Measures for Frailty Models
    22. 11.1. Introduction
    23. 11.2. The proposed goodness-of-fit test
    24. 11.3. Main results
    25. 11.4. Frailty models
    26. 11.5. Simulations
    27. 11.6. References
  8. List of Authors
  9. Index
  10. End User License Agreement
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