Statistical Topics and Stochastic Models for Dependent Data with Applications

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