Probability for Statisticians

• Main Author: Shorack, Galen R. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2000.
• Series: Springer Texts in Statistics,
• Subjects: Mathematics.; Probabilities.; Statistics.; Probability Theory and Stochastic Processes.; Statistics, general.

Probability for Statisticians is intended as a text for a one year graduate course aimed especially at students in statistics. The choice of examples illustrates this intention clearly. The material to be presented in the classroom constitutes a bit more than half the text, and the choices the autho...

Table of Contents:

• Measures
• Measurable Functions and Convergence
• Integration
• Derivatives via Signed Measures
• Measures and Processes on Products
• General Topology and Hilbert Space
• Distribution and Quantile Functions
• Independence and Conditional Distributions
• Special Distributions
• WLLN, SLLN, LIL, and Series
• Convergence in Distribution
• Brownian Motion and Empirical Processes
• Characteristic Functions
• CLTs via Characteristic Functions
• Infinitely Divisible and Stable Distributions
• Asymptotics via Empirical Proceses
• Asymptotics via Stein’s Approach
• Martingales
• Convergence in Law on Metric Spaces.