Probability for Statisticians

The choice of examples used in this text clearly illustrate its use for a one-year graduate course. The material to be presented in the classroom constitutes a little more than half the text, while the rest of the text provides background, offers different routes that could be pursued in the classroom, as well as additional material that is appropriate for self-study. Of particular interest is a presentation of the major central limit theorems via Steins method either prior to or alternative to a characteristic function presentation. Additionally, there is considerable emphasis placed on the quantile function as well as the distribution function, with both the bootstrap and trimming presented. The section on martingales covers censored data martingales.

Inhalt

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.