利用混合样本和序贯二项抽样对率进行区间估计的研究

A study on interval estimation of rates using sequential binomial sampling and pooled samples

目的探讨对较低的率做区间估计时如何利用混合样本和序贯二项抽样降低检测次数,节约成本。方法根据中心极限定理和δ方法(或Fisher信息量),利用正态近似给出总体率的置信区间,并通过理论分析和随机模拟,从区间的实际覆盖率、精度和检测次数等角度,对一些样本混合及检测方案进行测试。结果当nb(r,p)的参数r≥4时,本文给出的95%置信区间的实际覆盖率均可达到95%;为了达到指定的精度,由m=1可找到最小的r,增大r并适当增大混合样本中的样品个数m,可保持精度不变。结论利用混合样本方法并结合序贯二项抽样,可以有效减少检测次数,降低成本;对指定的估计精度,结合检测成本和样品采集成本,用本文的思路和方法可大致确定合适的样本混合及检测方案。

Objective To obtain interval estimation of lower rates using sequential binomial sampling and pooled samples for decreasing the numbers of test.Methods 95% approximate confident intervals are provided by using the central limit theorem and Delta method or Fisher information,and several pooling strategies are examined from the points of the correctness rate,precision,and the numbers of test by theoretical analysis and simulation using software MATLAB7.1.Results While the parameter r of nb（r,p）greater than 4,the correctness of 95%CI provided is accurately round about 95%;For given precise of 95%CI,the minimal r can be approximately decided by letting m=1,and the given precise of 95%CI can be retained while r and the number of individuals of pool increasing within some definite range.Conclusion The numbers of test can be evidently reduced by using pool sampling method and sequential binomial sampling,and for given precise of 95%CI,the pooling strategies can be deduced by taking the cost of sample testing and sample collecting into account.