Statistical Inferences for Stochasic Processes
Theory and Methods
- 1st Edition - December 8, 2014
- Author: Ishwar V. Basawa
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 9 3 3 - 0 7 2 9 - 6
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 9 6 1 4 - 2
Statistical Inference Stochastic Processes provides information pertinent to the theory of stochastic processes. This book discusses stochastic models that are increasingly used in… Read more
Statistical Inference Stochastic Processes provides information pertinent to the theory of stochastic processes. This book discusses stochastic models that are increasingly used in scientific research and describes some of their applications. Organized into three parts encompassing 12 chapters, this book begins with an overview of the basic concepts and procedures of statistical inference. This text then explains the inference problems for Galton–Watson process for discrete time and Markov-branching processes for continuous time. Other chapters consider problems of prediction, filtering, and parameter estimation for some simple discrete-time linear stochastic processes. This book discusses as well the ergodic type chains with finite and countable state-spaces and describes some results on birth and death processes that are of a non-ergodic type. The final chapter deals with inference procedures for stochastic processes through sequential procedures. This book is a valuable resource for graduate students.
Preface
List of Notation
Chapter 0 Introductory Examples of Stochastic Models
Example 1. A Random Walk Model for Neuron Firing
Example 2. Chain Binomial Models in Epidemiology
Example 3. A Population Growth Model
Example 4. A Spatial Model for Plant Ecology
Example 5. A Cluster Process for Population Settlements
Example 6. A Model in Population Genetics
Example 7. A Storage Model
Example 8. A Compound Poisson Model for Insurance Risk
Example 9. System Reliability Models
Example 10. A Model for Cell Kinetics
Example 11. Queueing Models for Telephone Calls
Example 12. Clustering Splitting Model for Animal Behaviour
Example 13. Prediction of Economic Time Series
Example 14. Signal Estimation
Bibliographical Notes
Part I Special Models
Chapter 1 Basic Principles and Methods of Statistical Inference
1. Introduction
2. The Likelihood Function and Sufficient Statistics
3. Frequency Approach
4. The Bayesian Approach
5. Asymptotic Inference
6. Nonparametric Methods
7. Sequential Methods
Bibliographical Notes
Chapter 2 Branching Processes
1. Introduction
2. The Galton-Watson Process
3. The Markov Branching Process
Bibliographical Notes
Complements
Chapter 3 Simple Linear Models
1. Introduction
2. Prediction
3. Filtering Problem
4. Parameter Estimation
5. Further Topics
Bibliographical Notes
Complements
Chapter 4 Discrete Markov Chains
1. Introduction
2. Finite Markov Chains
3. A Macro Model (Finite State Space)
4. Grouped Markov Chains (Finite State Space)
5. Countable State Space
Bibliographical Notes
Complements
Chapter 5 Markov Chains in Continuous Time
1. Introduction
2. Finite Markov Chains
3. Queueing Models
4. Pure Birth Process
5. The Birth and Death Process
Bibliographical Notes
Complements
Chapter 6 Simple Point Processes
1. Introduction
2. Homogeneous Poisson Process
3. Non-homogeneous Poisson Process
4. Compound Poisson Process
5. Further Topics
Bibliographical Notes
Complements
Part II General Theory
Chapter 7 Large Sample Theory for Discrete Parameter Stochastic Processes
1. Introduction
2. Estimation
3. Efficient Tests of Simple Hypotheses
4. Large Sample Tests
5. Optimal Asymptotic Tests of Composite Hypotheses
6. Further Topics
Bibliographical Notes
Complements
Chapter 8 Large Sample Theory for Continuous Parameter Stochastic Processes
1. Introduction
2. Observable Coordinates
3. The General Problem
4. Testing Hypotheses
5. Estimation
6. Estimating the Infinitesimal Generator for a Continuous Time Finite State Markov Process
7. Further Topics
Bibliographical Notes
Complements
Chapter 9 Diffusion Processes
1. Introduction
2. Diffusion Processes
3. Absolute Continuity of Measures for Diffusion Processes
4. Parameter Estimation in a Linear Stochastic Differential Equation
5. Asymptotic Likelihood Theory for Multidimensional Diffusion Processes
6. Hypotheses Testing for Parameters of Diffusion Processes
7. Sequential Estimation of the Parameters of a Diffusion Process
8. Sequential Test for Diffusion Processes
9. Bayes Estimation for Diffusion Processes
10. Further Topics
Bibliographical Notes
Complements
Part III Further Approaches
Chapter 10 Bayesian Inference for Stochastic Processes
1. Introduction
2. Preliminaries
3. The Bernstein-Von Mises Theorem
4. Asymptotic Behaviour of Bayes Estimators
5. Bayesian Testing
6. Further Topics
7. Proof of Tightness of Processes
Bibliographical Notes
Complements
Chapter 11 Nonparametric Inference for Stochastic Processes
1. Introduction
2. Nonparametric Estimation for Stochastic Processes
3. Nonparametric Tests for Stochastic Processes
4. Further Topics
Bibliographical Notes
Complements
Chapter 12 Sequential Inference for Stochastic Processes
1. Introduction
2. Sequential Estimation for Stochastic Processes
3. Sequential Tests of Hypotheses for Stochastic Processes
4. Sequential Tests for the Drift of Wiener Process
5. Further Topics
Bibliographical Notes
Complements
Appendix 1 Martingales
1. Martingales and Limit Theorems
2. A Random Central Limit Theorem for Martingales
3. Embedding Submartingales in Wiener Process with Drift
4. Structure of Continuous Parameter Martingales
Appendix 2 Stochastic Differential Equations
1. Stochastic Integrals
2. Central Limit Theorem for Vector-Valued Stochastic Integrals
3. Stochastic Differential Equations
Appendix 3 Proof of Sudakov's Lemma (Theorem 2.3) of Chapter 12
Appendix 4 Generalized Functions and Generalized Stochastic Processes
References
Index
- Edition: 1
- Published: December 8, 2014
- Language: English
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