鞍点逼近下相关差的置信区间构造  

Confidence interval construction of correlation difference under saddle point approximation

作　　者：王维贤 田茂再[2] WANG Wei-xian;TIAN Mao-zai(School of Mathematics and Statistics, University of Kashgar, Kashgar 844008, China;Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing 100872,China)

机构地区：[1]喀什大学数学与统计学院,新疆喀什844008 [2]中国人民大学应用统计科学研究中心,中国人民大学统计学院,北京100972

出　　处：《高校应用数学学报（A辑）》2019年第3期264-272,共9页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11861042);教育部人文社会科学重点研究基地重大项目“面向数据科学的统计建模、应用与评价研究”;中国人民大学科学研究基金(中央高校基本科研业务费专项资金)(18XNL012);新疆维吾尔自治区普通高等学校人文社会科学基地基金

摘　　要：相关差是医学中常用的重要指标,慢性病发病常用Poisson分布来拟合.使用鞍点逼近方法构造了相关差的置信区间,同时与传统的4种置信区间的构造方法,利用Monte Carlo模拟进行比较,最后用于实际数据分析.结果表明,鞍点逼近方法在大多数情况下,覆盖率较接近名义水平;在覆盖率差别不大时,鞍点逼近方法构造的区间长度较短;尤其在小样本下,鞍点逼近方法表现最好.所以鞍点逼近是统计量置信区间构造的一个好方法,可在各个领域内进行推广.Correlation difference is an important index commonly used in medicine.The incidence of chronic diseases is usually fitted by Poisson distribution,the confidence interval of the correlation difference is constructed by using the saddle point approximation method.At the same time,it is compared with the traditional 4 confidence interval construction methods by using the Monte Carlo simulation.Finally,it is used for the actual data analysis.The results show that the saddle point approximation method is near the nominal level in most cases,and the interval length of saddle point approach is shorter when the difference of coverage is small;especially in small samples,the saddle point approach is the best.So saddle point approximation is a good method for constructing confidence intervals of statistics and can be generalized in various fields.

关 键 词：相关差 鞍点逼近 置信区间 POISSON分布 MONTE CARLO模拟 

分 类 号：O212.4[理学—概率论与数理统计]