Asymptotic Stochastics An Introduction with a View towards Statistics /
This textbook, which is based on the second edition of a book that has been previously published in German language, provides a comprehension-oriented introduction to asymptotic stochastics. It is aimed at the beginning of a master's degree course in mathematics and covers the material that can...
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| Format: | Elektronski eKnjiga |
| Jezik: | angleščina |
| Izdano: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
2024.
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| Izdaja: | 1st ed. 2024. |
| Serija: | Mathematics Study Resources,
10 |
| Teme: | |
| Online dostop: | https://doi.org/10.1007/978-3-662-68923-3 |
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Kazalo:
- Preface
- List of Symbols
- 1 Prerequisites from Probability Theory
- 2 A Poisson Limit Theorem for Triangular Arrays
- 3 The Method of Moments
- 4 A Central Limit Theorem for Stationary m-Dependent Sequences
- 5 The multivariate normal distribution
- 6 Convergence in Distribution and Central Limit Theorem in Rd
- 7 Empirical Distribution Function
- 8 Limit Theorems for U-Statistics
- 9 Basic Concepts of Estimation Theory
- 10 Maximum Likelihood Estimation
- 11 Asymptotic (relative) efficiency of estimators
- 12 Likelihood Ratio Tests
- 13 Probability Measures on Metric Spaces
- 14 Convergence of Distributions in Metric Spaces
- 15 Wiener Process, Donsker’s Theorem, and Brownian Bridge
- 16 The Space D[0,1], Empirical Processes
- 17 Random Elements in Separable Hilbert Spaces
- Afterword
- Solutions to the Problems
- Bibliography
- Index.