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Название: Basic Concepts of Probability and Statistics (Classics in Applied Mathematics)

Авторы: Hodges J., Lehmann E.

Аннотация:

It is often pointed out that the modern theory of statistics requires probability theory, which in turn rests upon measure theory. As a result, all the "calculus-based" statistics textbooks known to me - like Bartoszynski/Niewiadomska-Bugaj 1996, Berger/Casella 2002, Hogg/Craig 1995, Rohatgi 1976, Roussas 1973, to name just a few - always gloss over various essential points because their rigorous exposition usually requires measure theory and nobody has yet succeeded in devising alternative "elementary" proofs for them based on calculus alone. I have therefore always considered it a thankless task to seriously explain statistics while not even invoking calculus. Nevertheless, the reading of Hodges/Lehmann's remarkable book has opened my eyes on how much meaningful statistical thinking is already possible by utilizing only high school algebra! Added to my embarrassment is the fact that the fist edition of their book was published in 1964 and that in the last five years I have taught various introductory statistics courses without the benefit of knowledge of Hodges/Lehmann. To be sure, there are lots of statistics textbooks in the market (both in English and in Chinese, in case you can also read in my native language) without using calculus. But, as far as I have read, all of them except Hodges/Lehmann are essentially "cookbooks" which are more suitable for training robots rather than inquisitive minds eager to follow careful reasoning whenever available. Not surprisingly, to make their book honest and rigorous Hodges and Lehmann restrict themselves to discrete random phenomena. But it is surprising that their treatment is not thereby made shallow. There is no point for me to recapitulate the book's contents as the interested reader can easily obtain fuller information via Amazon's superb "search inside the book" option. It suffices to say that I'm most impressed by its Part II on estimation and hypotheses testing. Every topic is gently but thoroughly presented through carefully designed examples which pave the way for the elegant proofs of all the book's formulas so well that those great intellectual achievements like the Neyman-Pearson Fundamental Lemma begin to appear like something which every person accustomed to careful reasoning should have been able to discover by himself/herself. Moreover, even practitioners and teachers of statistics might occasionally find something unexpected in the author's numerous remarks on various statistical fine points and pitfalls which could also mislead the relatively experienced. These clarifications will remind us that the authors are not only excellent educators but also eminent statisticians in the first place. And the beginning student should consider it a good fortunate that a world-acclaimed author of advanced books on estimation and testing like Lehmann should so seriously take this elementary work that "each section, nearly each sentence, was vigorously debated, drafted, and subjected to additional debate" with his Berkeley colleague J.L.Hodges. And the result is a masterly exposition with amazing clarity.Currently I'm teaching some four hundred business-school students introductory statistics out of a textbook in Chinese which is vastly inferior to that of Hodges/Lehmann. After reading the masters' work, I really feel sorry for my students. Not only it is too late to change the textbook but also there is no Chinese translation of Hodges/Lehmann (it has been translated into Italian, Hebrew, Danish and Farsi ). And unfortunately most of my students will fear reading an English text no less than studying statistics itself. So I couldn't resist giving an advice to the lucky English-speaking beginning statistics students: study calculus and even measure theory if you can, for that will enormously help your statistics education. But if you are anxious to understand the fundamental concepts of statistics right now without already equipping yourself of START TRANSACTION WITH CONSISTENT SNAPSHOT; /* 489 = 16e914a6aadf4a7afd271d09de1f8fe8