Bias-corrected estimators for proportion of true null hypotheses: application of adaptive FDR-controlling in segmented failure data

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.

Keywords: 62F99; 62N99; 62P30; Multiple hypotheses testing; adaptive Benjamini–Hochberg algorithm; mean mileage to failure; p-value.