Mathematical Statistics by S. Wilks (PDF)

Description

This book contains S. S. Wilks’ lessons on mathematical statistics, and will make an excellent addition to the bookshelf of anyone with an interest in the subject. Preface: ‘Most of the mathematical theory of statistics in its present state has been developed during the past twenty years. Because of the variety of scientific fields in which statistical problems have arisen, the original contributions to this branch of applied mathematics are widely scattered in scientific literature. Most of the theory still exists only in original form. During the past few years the author has conducted a two-semester course at Princeton University for advanced undergraduates and beginning graduate students in which an attempt has been made to give the students an introduction to the more recent developments in the mathematical theory of statistics. The subject matter for this course has been gleaned, for the most part, from periodical literature. Since it is impossible to cover in detail any large portion of this literature in two semesters, the course has been held primarily to the basic mathematics of the material, with just enough problems and examples for illustrative and examination purposes…’

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I recommend you do not buy the green-covered 15 March 2007 Buck Press printing; I returned two copies after checking them and finding an important page left out.I purchased two new copies from Amazon.com of the printing by Buck Press, dated 15 March 2007, with the light green cover decorated with billiard balls. Both copies were missing pages 149-150. Buck Press photocopied an earlier publisher’s printing: you can see unerased pencil marks on the table of contents from an earlier reader. Unfortunately, the original used for the 2007 re-print was damaged.I think the defect is important: the author, Samuel Stanley Wilks (1906-1964), proved a key theorem in 1938 showing how to approximate the variation in likelihood ratios. It’s a crucial tool calculating confidence bounds for maximum likelihood estimates. Wilks’ theorem begins on page 149 and continues past 150. The 2 missing pages erase the book’s value.The rest of the book is typeset using a typewriter manuscript, and is an introduction to theoretical statistics which has since been done well in better-looking texts. I say use one of them instead. Until Buck Press reprints a good copy of the book, I suggest that you borrow a library copy of the original printing, or purchase a used copy from a different publisher that has pages 149-150 intact (which is what I did). Alternative texts are Castella & Berger ‘

⭐, or Bain & Engelhardt ‘

⭐.

⭐Note that this Kindle version from Buck Press is different from the version published by Wiley in 1962 (this review might also apply to the hardcopy reprint by Buck Press). In the Wiley version, there are 18 chapters while the Buck Press has only 11 chapters. Also the Buck Press version for the Kindle is missing section 7.2 on likelihood ratio tests (might be related to the review by TomCosmic). The preface to the Wiley version does mention the existence of an earlier version of the material in lithoprinted form issued by the Princeton University; I highly suspect that the Buck Press version is based on a copy of this earlier version. Also in the Kindle version, the complicated formulas are scanned images from typewritten version, and some symbols don’t render properly on Kindle (you’ll just see boxes for these symbols).In any case, if you are looking for the 1962 Wiley version of the book (for which I would give a 5-star rating), your best bet is probably to look for a used copy.

⭐I bought the original 1962 version and find it thrilling to see the amount of work that went into writing it, and the amount of time one might spend on reading it. Strictly for a very slow, deliberate, technical read on Mathematical Statistics. I’ve been told that at one time, the book was the standard University text on the subject. Nice for a collector. But so glad books have gotten a lot better!

⭐経済学の大学院生だった時、指導教授から「経済学に必要な統計学の全てが書かれている名著なのに、絶版で残念だ」と言われたことがありました。その後、大学院留学した時、統計学部から統計学セミナーの案内メールが来た時に、前提となる知識として数冊挙げられており、その中の1冊としてこの教科書がありました。絶版してもなお引用される名著であることは間違いありません。それゆえの再版なのでしょう。Hogg & Craigよりも1段階ないし2段階高いレベルの教科書ですが、大学院レベルの統計学としては数学・統計学専攻であれ、或いは経済学専攻であれ、Hogg & Craigでは足りません。それゆえ、大学院で統計学を使う方には強くお勧めしたいところなのですが、誰かが持っていた1943年当時のタイプライター活版方式で印字された形での書物に、たとえば目次のところにチェック印がついていたり、インクが漏れて文字が見えなかったりしているところもあるので、非常に読みづらいのが、非常に残念です。ちなみに、この書物はその後、もっと綺麗な活字で印刷されていたことがあり、そちらの方が再版されなかったのは何故なのか、疑問が残ります。古典的名著であるサミュエル・ウィルクスの『数理統計学』をどうしても見ておきたい人にはお勧めですが、この本を使って大学院レベルに到達するまで統計学を自学自習するという目的には、少々難があります。というわけで、内容自体は5つ星ですが、活字の読みにくさや私物的なチェック印・インク漏れなどから、3つ星にしておきます。

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