Probability and Measure
Probability and Measure
复制标题
DOI：
10.1007/978-0-387-93839-4_1
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
R. Keener
中科院分区：
文献类型：
--
作者：
R. Keener
许多统计推断的理论可以在不详细了解概率或测度理论的情况下理解。本书对这些问题的论述并不严谨。但一些基本的知识是非常有用的。统计学中的许多文献都使用了测度理论，不熟悉基本符号的人无法使用。此外，测量理论的符号允许合并离散和连续随机变量的结果。此外，该符号可以处理涉及删失或截断的有趣且重要的应用，其中感兴趣的随机变量既不是离散的也不是连续的。最后，测度论的语言对于正确地陈述许多结果是必要的。在续集中，测度理论的细节通常在证明中被淡化或忽略，但演示足够详细，任何具有良好概率背景的人都应该能够填补任何缺失的细节。
Much of the theory of statistical inference can be appreciated without a detailed understanding of probability or measure theory. This book does not treat these topics with rigor. But some basic knowledge of them is quite useful. Much of the literature in statistics uses measure theory and is inaccessible to anyone unfamiliar with the basic notation. Also, the notation of measure theory allows one to merge results for discrete and continuous random variables. In addition, the notation can handle interesting and important applications involving censoring or truncation in which a random variable of interest is neither discrete nor continuous. Finally, the language of measure theory is necessary for stating many results correctly. In the sequel, measure-theoretic details are generally downplayed or ignored in proofs, but the presentation is detailed enough that anyone with a good background in probability should be able to fill in any missing details.