二项分布下基于鞍点逼近的总体成数置信区间的构造  

Construction of Confidence Intervals for the Whole Percentage Based on Saddle Point Approximations under Binomial Distribution

作　　者：夏丽丽 田茂再[2,3] 朱钰 XIA Li-li;TIAN Mao-zai;ZHU Yu(School of Applied Mathematics and Science,Beijing University of Technology,Beijing 100872,China;Center for Applied Statistics Renmin University of China,Beijing 100872,China;School of Statistics,Renmin University of China,Beijing 100872,China;School of Statistics,Xi'an University of Finance and Economics,Xi'an 710100,China)

机构地区：[1]北京工业大学应用数理学院,北京100872 [2]中国人民大学应用统计科学研究中心,北京100872 [3]中国人民大学统计学院,北京100872 [4]西安财经大学统计学院,陕西西安710100

出　　处：《统计与信息论坛》2019年第9期3-9,共7页Journal of Statistics and Information

基　　金：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资助)项目《大数据分析的稳健统计理论与应用研究》(18XNL012)

摘　　要：面对总体成数置信区间的估计问题,可以采用二项分布下基于鞍点逼近的方法来构造总体成数的置信区间,这种方法为总体成数的区间估计提供了一种新的途径,将其和传统的区间估计方法比较,即正态近似法和枢轴量法进行比较。蒙特卡洛模拟和实例分析的结果为:在几种不同的置信区间构造方法中,小样本情况下,鞍点逼近方法构造的总体成数的置信区间长度相对较短,覆盖率最接近名义水平;大样本下,鞍点逼近方法整体表现最优。因此,可以得到鞍点逼近法对总体成数置信区间的估计较为精确,尤其是小样本情况下更为适用的结论。Facing the problem of estimating the percentage confidence interval,the method of saddle point approximation based on binomial distribution can be used to construct the confidence interval of the whole percentage.It provides a new way for the interval estimation of the whole percentage.Comparing with the traditional interval estimation method including the normal approximation method and the pivot method,the results of Monte Carlo simulation and case analysis are as follows:in several different confidence interval construction methods,the confidence interval of the whole percentage of constructs constructed by the saddle point approximation method is relatively short in small sample cases,and the coverage rate is closest to the nominal level.For the large sample,the saddle point approximation method is the best overall performance.Therefore,it can be obtained that the saddle point approximation method is more accurate in estimating the whole percentage interval,especially in the case of small samples.

关 键 词：二项分布 鞍点逼近 置信区间 蒙特卡洛模拟 

分 类 号：C812[社会学—统计学]