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Strong Approximations in Probability and Statistics.
Strong Approximations in Probability and Statistics.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York : Budapest :
Academic Press ; Akad�emiai Kiad�o,
�1981.
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| Colección: | Probability and mathematical statistics.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Strong Approximations in Probability and Statistics; Copyright Page; Table of Contents; Preface; Introduction; Chapter 1. Wiener and some Related Gaussian Processes; 1.0 On the notion of a Wiener process; 1.1 Definition and existence of a Wiener process; 1.2 How big are the increments of a Wiener process?; 1.3 The law of iterated logarithm for the Wiener process; 1.4 Brownian bridges; 1.5 The distributions of some functional of the Wiener and Brownian bridge processes; 1.6 The modulus of non-differentiability of the Wiener process
- 2.1 A proof of Donsker's theorem with Skorohod's embedding scheme2.2 The strong invariance principle appears; 2.3 The stochastic Geyser problem as a lower limit to the strong invariance problem; 2.4 The longest runs of pure heads and the stochastic Geyser problem; 2.5 Improving the upper limit; 2.6 The best rates emerge; Supplementary remarks; Chapter 3. A Study of Partial Sums with the Help of Strong Approximation Methods; 3.0 Introduction; 3.1 How big are the increments of partial sums of I.I.D.R.V. when the moment generating function exists?
- 3.2 How big are the increments of partial sums of I.I.D.R.V. when the moment generating function does not exist?3.3 How small are the increments of partial sums of I.I.D.R.V.?; 3.4 A summary; Supplementary remarks; Chapter 4. Strong Approximations of Empirical Processes by Gaussian Processes; 4.1 Some classical results; 4.2 Why should the empirical process behave like a Brownian bridge?; 4.3 The first strong approximations of the empirical process; 4.4 Best strong approximations of the empirical process; 4.5 Strong approximation of the quantile process; Supplementary remarks
- Chapter 5. A Study of Empirical and Quantile Processes with the Help of Strong Approximation Methods5.0 Introduction; 5.1 The law of iterated logarithm for the empirical process; 5.2 The distance between the empirical and the quantile processes; 5.3 The law of iterated logarithm for the quantile process; 5.4 Asymptotic distribution results for some classical functionals of the empirical process; 5.5 Asymptotic distribution results for some classical functionals of the quantile process