Applications of the representative points in statistical simulations  

作　　者：FANG KaiTai ZHOU Min WANG WenJun 

机构地区：[1]Division of Science and Technology, Beijing Normal University-Hong Kong Baptist University,United International College [2]Institute of Applied Mathematics, Academy of Mathematics and Systems Science,Chinese Academy of Sciences [3]Department of Mathematics, Hainan Normal University

出　　处：《Science China Mathematics》2014年第12期2609-2620,共12页中国科学：数学（英文版）

基　　金：supported by the Special Research Foundation from the Chinese Academyof Sciences;the Beijing Normal University-Hong Kong Baptist University United International College Research(Grant No.R201409);National Natural Science Foundation of China(Grant No.11261016)

摘　　要：The paper gives a new approach to statistical simulation and resampling by the use of numbertheoretic methods and representative points. Resempling techniques take samples from an approximate population. The bootstrap suggests to use a random sample to form an approximate population. We propose to construct some approximate population distribution by the use of two kinds of representative points, and samples are taken from these approximate distributions. The statistical inference is based on those samples. The statistical inference in this paper involves estimation of mean, variance, skewness, kurtosis, quantile and density of the population distribution. Our results show that the new method can significantly improve the results by the use of Monte Carlo methods.The paper gives a new approach to statistical simulation and resampling by the use of numbertheoretic methods and representative points. Resempling techniques take samples from an approximate population. The bootstrap suggests to use a random sample to form an approximate population. W＇e propose to construct some approximate population distribution by the use of two kinds of representative points, and samples are taken from these approximate distributions. The statistical inference is based on those samples. The statistical inference in this paper involves estimation of mean, variance, skewness, kurtosis, quantile and density of the population distribution. Our results show that the new method can significantly improve the results by the use of Monte Carlo methods.

关 键 词：BOOTSTRAP kernel density estimation normal distribution representative points RESAMPLING statistical simulation 

分 类 号：O212.1[理学—概率论与数理统计] P48[理学—数学]