Volume I of this two-volume text and reference work begins by providing a foundation in measure and integration theory. It then offers a systematic introduction to probability theory, and in particular, those parts that are used in statistics. This volume discusses the law of large numbers for independent and non-independent random variables, transforms, special distributions, convergence in law, the central limit theorem for normal and infinitely divisible laws, conditional expectations and martingales. Unusual topics include the uniqueness and convergence theorem for general transforms with...

Part of a two-volume text and reference work, this volume concentrates on the applications of probability to statistics. Topics include: the art of calculating densities of complicated transformations of random vectors; exponential models; consistency of maximum estimators; and other topics.