Mathematical Statistics and Stochastic Processes
Publication Date: April 2012 Hardback 304 pp.
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 up-to-date information on the relevant topics of theory of probability, estimation, confidence intervals, non-parametric statistics and robustness, second-order 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.
Part 1. Mathematical Statistics
1. Introduction to Mathematical Statistics.
2. Principles of Decision Theory.
3. Conditional Expectation.
4. Statistics and Sufficiency.
5. Point Estimation.
6. Hypothesis Testing and Confidence Regions.
7. Asymptotic Statistics.
8. Non-Parametric Methods and Robustness.
Part 2. Statistics for Stochastic Processes
9. Introduction to Statistics for Stochastic Processes.
10. Weakly Stationary Discrete-Time Processes.
11. Poisson Processes – A Probabilistic and Statistical Study.
12. Square-Integrable Continuous-Time Processes.
13. Stochastic Integration and Diffusion Processes.
14. ARMA Processes.
Part 3. Supplement
16. Elements of Probability Theory.
About the Authors
Denis Bosq is Emeritus Professor at the Laboratory of Statistics, Theory and Application (LSTA) at UPMC in Paris. He is the author of many books and papers on statistics, theory and probability.