数学统计学中的现代概念和定理

English | PDF | 1986 | 168 Pages | ISBN : 1461293324 | 11.3 MB

With the rapid progress and development of mathematical statistical methods, it is becoming more and more important for the student, the in­ structor, and the researcher in this field to have at their disposal a quick, comprehensive, and compact reference source on a very wide range of the field of modern mathematical statistics. This book is an attempt to fulfill this need and is encyclopedic in nature. It is a useful reference for almost every learner involved with mathematical statistics at any level, and may supple­ ment any textbook on the subject. As the primary audience of this book, we have in mind the beginning busy graduate student who finds it difficult to master basic modern concepts by an examination of a limited number of existing textbooks. To make the book more accessible to a wide range of readers I have kept the mathematical language at a level suitable for those who have had only an introductory undergraduate course on probability and statistics, and basic courses in calculus and linear algebra. No sacrifice, how­ ever, is made to dispense with rigor. In stating theorems I have not always done so under the weakest possible conditions. This allows the reader to readily verify if such conditions are indeed satisfied in most applications given in modern graduate courses without being lost in extra unnecessary mathematical intricacies. The book is not a mere dictionary of mathematical statistical terms.

随着数学统计方法的迅速进步和发展，这个领域内的学生、教师和研究者越来越需要有一本快速、全面且精炼的现代数学统计学范围广泛的参考书。这本书试图满足这一需求，并具有百科全书性质。它几乎对所有任何层次的学习者都是有用的参考资料，并可能补充任何关于该主题的教科书。作为本书的主要受众，我们想到的是那些忙于学习数学统计学的初学者研究生，他们很难通过研究一些现有的教科书来掌握现代的基本概念。为了让这本书更适合广泛的读者群体，我保持了对于那些只上过概率与统计入门课程以及基本的微积分和线性代数课程的学生来说，足够的数学语言水平。然而，并没有因为这一点而牺牲掉严谨性。在陈述定理时，我没有总是用最弱的条件来表述。这使得读者能够很容易地验证，在现代研究生课程中给出的应用实例满足这些条件，同时避免陷入不必要的数学细节。这本书不仅仅是数学统计学术语的字典而已。

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