Book description
Generally, books on mathematical statistics are restricted to the case of independent identically distributed random variables. In this book however, both this case AND the case of dependent variables, i.e. statistics for discrete and continuous time processes, are studied. This second case is very important for today's practitioners.
Mathematical Statistics and Stochastic Processes is based on decision theory and asymptotic statistics and contains uptodate information on the relevant topics of theory of probability, estimation, confidence intervals, nonparametric statistics and robustness, secondorder processes in discrete and continuous time and diffusion processes, statistics for discrete and continuous time processes, statistical prediction, and complements in probability.
This book is aimed at students studying courses on probability with an emphasis on measure theory and for all practitioners who apply and use statistics and probability on a daily basis.
Table of contents
 Cover
 Title Page
 Copyright
 Preface

Part 1: Mathematical Statistics
 Chapter 1: Introduction to Mathematical Statistics
 Chapter 2: Principles of Decision Theory
 Chapter 3: Conditional Expectation
 Chapter 4: Statistics and Sufficiency

Chapter 5: Point Estimation
 5.1. Generalities
 5.2. Sufficiency and completeness
 5.3. The maximumlikelihood method
 5.4. Optimal unbiased estimators
 5.5. Efficiency of an estimator
 5.6. The linear regression model
 5.7. Exercises
 Chapter 6: Hypothesis Testing and Confidence Regions
 Chapter 7: Asymptotic Statistics
 Chapter 8: NonParametric Methods and Robustness

Part 2: Statistics for Stochastic Processes
 Chapter 9: Introduction to Statistics for Stochastic Processes
 Chapter 10: Weakly Stationary DiscreteTime Processes
 Chapter 11: Poisson Processes – A Probabilistic and Statistical Study
 Chapter 12: SquareIntegrable ContinuousTime Processes
 Chapter 13: Stochastic Integration and Diffusion Processes
 Chapter 14: ARMA Processes
 Chapter 15: Prediction
 Part 3: Supplement

Appendix: Statistical Tables
 A1.1. Random numbers
 A1.2. Distribution function of the standard normal distribution
 A1.3. Density of the standard normal distribution
 A1.4. Percentiles (tp) of Student’s distribution
 A1.5. Ninetyfifth percentiles of Fisher–Snedecor distributions
 A1.6. Ninetyninth percentiles of Fisher–Snedecor distributions
 A1.7. Percentiles (χ2p) of the χ2 distribution with n degrees of freedom
 A1.8. Individual probabilities of the Poisson distribution
 A1.9. Cumulative probabilities of the Poisson distribution
 A1.10. Binomial coefficients Ckn for n ≤ 30 and 0 ≤ k ≤ 7
 A1.11. Binomial coefficients Ckn for n ≤ 30 and 8 ≤ k ≤ 15
 Bibliography
 Index
Product information
 Title: Mathematical Statistics and Stochastic Processes
 Author(s):
 Release date: May 2012
 Publisher(s): Wiley
 ISBN: 9781848213616
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