常见数字特征估计量的渐进行为研究

Study on the asymptotic behavior of common digital feature estimatorsAbstract Asymptotic analysis is a method to describe the behavior of a function nearits limit.The method of asymptotic analysis has been applied in many scientific fields.Instatistics,asymptotic theory provides limited sample statistics of approximate probabilitydistributions,such as likelihood ratio statistics and deviations in the expected values.Asymptotic analysis is also a key tool to explore ordinary and partial differential equationsin mathematical modeling of real world phenomena.Random variables are divided into discrete random variables and non discreterandom variables according to their values.All possible values can be listed one by one ina certain order.Such random variables are called discrete random variables.If possiblevalues are full of an interval and cannot be listed one by one in order,such randomvariables are called non discrete random variables.If random variables are continuous,there is a distribution curve.There is a specialand very common distribution,and its distribution curve is very regular,that is,normaldistribution.The normal distribution curve depends on some characterizations of therandom variable,the most important of which are the average value and the differencedegree.Next,this paper will introduce the origin,proof and related applications ofcommon digital feature quantity in detail.This paper is divided into three parts:In the first part of this paper,the definition and application of mathematicalexpectation,variance,quantile,coefficient of kurtosis,covariance and each commoncharacteristic quantity are introduced and proved by examples.In the second part of this paper,we introduce the related theorem of the law of largenumbers and the related theorem and formula reasoning of the central limit theorem,andcarry out random simulation.Finally,we use MATLAB to realize the drawing.The third part introduces the asymptotic properties of variance.Keywords mathematical expectation variance quantilekurtosis coefficientcovariance law of large numbers.central limit theorem Normal distribution.