ABSTRACT

Two recently introduced model-based bias-corrected estimators for proportion of true null hypotheses (${\pi }_0$) under multiple hypotheses testing scenario have been restructured for random observations under a suitable failure model, available for each of the common hypotheses. Based on stochastic ordering, a new motivation behind formulation of some related estimators for ${\pi }_0$ is given. The reduction of bias for the model-based estimators are theoretically justified and algorithms for computing the estimators are also presented. The estimators are also used to formulate a popular adaptive multiple testing procedure. Extensive numerical study supports superiority of the bias-corrected estimators. The necessity of the proper distributional assumption for the failure data in the context of the model-based bias-corrected method has been highlighted. A case-study is done with a real-life dataset in connection with reliability and warranty studies to demonstrate the applicability of the procedure, under a non-Gaussian setup. The results obtained are in line with the intuition and experience of the subject expert. An intriguing discussion has been attempted to conclude the article that also indicates the future scope of study.

摘要

两个最近引入的基于模型的偏差校正估计器用于真零假设的比例（${\pi }_0$) 在多个假设下的测试场景已被重组，以在合适的故障模型下进行随机观察，可用于每个常见假设。基于随机排序，制定一些相关估计量的新动机${\pi }_0$给出。基于模型的估计量的偏差减少在理论上是合理的，并且还提出了计算估计量的算法。估计器还用于制定流行的自适应多重测试程序。广泛的数值研究支持偏差校正估计量的优越性。已经强调了在基于模型的偏差校正方法的背景下对故障数据进行适当分布假设的必要性。在非高斯设置下，使用与可靠性和保修研究相关的真实数据集进行案例研究，以证明该程序的适用性。所得结果符合课题专家的直觉和经验。一个有趣的讨论试图结束这篇文章，这也表明了未来的研究范围。