Probability and Statistical Inference. Robert Bartoszynski

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Preface to Second Edition

      The first edition of this book was published in 1996. Since then, powerful computers have come into wide use, and it became clear that our text should be revised and material on computer‐intensive methods of statistical inference should be added. To my delight, Steve Quigley, Executive Editor of John Wiley and Sons, agreed with the idea, and work on the second edition began.

      Unfortunately, Robert Bartoszyński passed away in 1998, so I was left to carry out this revision by myself. I revised the content by creating a new chapter on random samples, adding sections on Monte Carlo methods, bootstrap estimators and tests, and permutation tests. More problems were added, and existing ones were reorganized. Hopefully nothing was lost of the “spirit” of the book which Robert liked so much and of which he was very proud.

      This book is intended for seniors or first‐year graduate students in statistics, mathematics, natural sciences, engineering, and any other major where an intensive exposure to statistics is necessary. The prerequisite is a calculus sequence that includes multivariate calculus. We provide the material for a two‐semester course that starts with the necessary background in probability theory, followed by the theory of statistics.

      What distinguishes our book from other texts is the way the material is presented and the aspects that are stressed. To put it succinctly, understanding “why” is prioritized over the skill of “how to.” Today, in an era of undreamed‐of computational facilities, a reflection in an attempt to understand is not a luxury but a necessity.

      Probability theory and statistics are presented as self‐contained conceptual structures. Their value as a means of description and inference about real‐life situations lies precisely in their level of abstraction—the more abstract a concept is, the wider is its applicability. The methodology of statistics comes out most clearly if it is introduced as an abstract system illustrated by a variety of real‐life applications, not confined to any single domain.

Depending on the level of the course, the instructor can select topics and examples, both in the theory and in applications. These can range from simple illustrations of concepts, to introductions of whole theories typically not included in comparable textbooks (e.g., prediction, extrapolation, and filtration in time series as examples of use of the concepts of covariance and correlation). Such additional, more advanced, material (e.g., Chapter 5 on Markov Chains) is marked with asterisks. Other examples are the proof of the extension theorem (Theorem 6.2.4), showing that the cumulative distribution function determines the measure on the line; the construction of Lebesgue, Riemann–Stieltjes, and Lebesgue–Stieltjes integrals; and the explanation of the difference between double integral and iterated integrals (Section 8.3).

      In the material that is seldom included in other textbooks on mathematical statistics, we stress the consequences of nonuniqueness of a sample space and illustrate, by examples, how the choice of a sample space can facilitate the formulation of some problems (e.g., issues of selection or randomized response). We introduce the concept of conditioning with respect to partition (Section 4.4); we explain the Borel–Kolmogorov paradox by way of the underlying measurement process that provides information on the occurrence of the condition (Example 7.22); we present the Neyman–Scott theory of outliers (Example 10.4); we give a new version of the proof of the relation between mean, median, and standard deviation (Theorem 8.7.3); СКАЧАТЬ