摘 要统计学这门学科是十分悠久的。人们大多数认为，它开始于古希腊科学家亚里士多德的理论研究。在通过 2000 多年的开发后，统计最少经过了三个阶段。所谓“数学”和“统计学”不是一门新的统计学科，而是一个包含所有新的数据收集和分析方法的综合概念。以统计学这门学科的广义角度来看，估计量是观测数据计算并且计算出已知量估计的基础上订制的规则。一次估计是应用一组已知输入的结果。咱们经过一些抉择准绳从中抉择更好的估计量，然而时常很难说一个估计量要比另外一个更好。本文分为四个部分：第一部分介绍了常见的估计量，着重解释了了详细的参数估计和非参数估计，第二部分阐述了常用的不等式。详细写出了每个不等式的定义以及对他的证明。第三部分运用了之前的知识点，阐述及证明常见估计量的精度估计的性质，总结出无偏性，相合性，有效性。第四部分介绍了什么是偏差以及运用了前面几个部分总结的知识对大偏差相关知识进行推导。关键词：参数估计 非参数估计 Chebyshev 不等式 伯努利序列 大偏差技术AbstractStatistics is a very old science. It is generally believed that its academic research began in the Aristotelian era of ancient Greece and has a history of more than 2,300 years. It originated from the study of social and economic issues. Therefore, "mathematical statistics" is not a single new statistical theme. Rather, it is a comprehensive term for all the new methods of collecting and analyzing data formed by statistics in the third development stage. Probability theory is the theoretical basis of mathematical statistical methods, but it does not belong to the category of statistics, but belongs to the category of mathematics.In statistics, an estimator is a rule to calculate the estimated value of a known quantity based on the observation data. Estimators are sometimes called estimators, which are used to estimate unknown general parameters.One-time estimation refers to the result of applying this function to a set of known data sets to find the function. For ...
