在多重假设检验中, 对原假设为真的比例或数量的估计是一个基础性问题. 一类估计方法是基于排序$p$值的图方法, 由Schweder 和Spj$\varphi$tvoll(1982)首次提出. 但是这类方法只 利用了特定切点$p$值的信息, 当原假设和备择假设差异较小时, 现有方法的有效性会降低. 文章通过利用所有原假设$p$ 值的信息, 对估计进行了改进. 由于利用了更多的信息, 改进后的估计更有效. 数值模拟结果表明, 文章所提出的估计方法比现有方法有效性更好, 最后将所提出的方法应用到实际数据分析中.

Estimation for proportion or number of true null hypotheses is an essential task in multiple hypothesis test. One type of estimating methods is based on the graphic of the sorted $p$-values first proposed by Schweder and Spj$\varphi$tvoll(1982). But these methods only utilize the information of a specific cutpoint $p$-value, existing methods may lose efficiency when the deviation between null hypothesis and alternative hypothesis is small. In this paper, we improve estimating methods by taking all information of $p$-values on the null hypotheses. Improved methods are more accurate and efficient than corresponding original methods due to more information can be used. Compared with the existing methods, the accuracy of the proposed methods is competitive through numerical study.