控制混合方向误差的最优方法  

Optimal procedure for controlling the mixed directional error

作　　者：路万忠[1] LU Wanzhong(School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, Chin)

机构地区：[1]上海财经大学统计与管理学院,上海200433

出　　处：《华中师范大学学报（自然科学版）》2018年第2期172-182,共11页Journal of Central China Normal University：Natural Sciences

摘　　要：假定有很多双尾备择假设需要同时检验,一旦零假设被拒绝,就需要进行方向性决策.在这种情况下,相较于常用的错误率FDR,混合方向错误率mdFDR更受欢迎,因为后者控制由所有拒绝所引起的第Ⅰ类、第Ⅲ类错误比例之和的期望.现有文献介绍了带方向决策的BH方法(dBH procedure),该方法是带有依据检验统计量的符号而作出方向决策的BH线性检验方法,可在显著水平α下控制mdFDR.除dBH方法外,由Sarkar和Zhou提出的一个方法(SZ procedure)也能控制mdFDR.他们从贝叶斯观点证明了其方法的最优性.本文从频率学派观点,即假定假设分布可从数据获知,来讨论SZ方法的最优性.根据讨论,SZ方法在控制mdFDR及正确地断言更多非零假设的意义上依然是最优的.模拟结果进一步验证了分析结果是成立的,并验证了SZ方法较之于dBH方法更为有效.Suppose there are a large scale hypotheses with two-sided alternatives to be tested simultaneously.The directional decision is required to be made once a null hypothesis is rejected.In this case the mixed directional false discovery rate（mdFDR）is preferable to the usual FDR for the former allowing to control the sum of expected proportions of Type Ⅰ and Type Ⅲ errors among all rejections.Existing literature showed the directional BH procedure（dBH procedure）,which is the BH linear step-up procedure being with directional decisions according to the signs of testing statistics,can control mdFDR at the significant levelα.Besides the dBH procedure,aprocedure proposed by Sarkar and Zhou（SZ procedure）also can control the mdFDR.Sarkar and Zhou showed the optimality of their procedure from the Bayesian point of view.In this paper,we discuss the optimality of the SZ procedure from the frequentist point of view which assumes the hypotheses distributions can be learned from the data.By our discussion,the SZ procedure is still optimal in the sense of controlling mdFDR and correctly declaring more non-null hypotheses.Simulation results further verify that the analytical results hold and the SZ procedure is more efficient than the dBH procedure.

关 键 词：mdFDR 最优 很多假设 带方向性决策 

分 类 号：O212.4[理学—概率论与数理统计]