Bias corrected estimators for proportion of true null hypotheses under exponential model: Application of adaptive FDR-controlling in segmented failure data

TL;DR

This paper develops bias-corrected estimators for the proportion of true null hypotheses under an exponential model, improving adaptive FDR control in segmented failure data with theoretical justification and practical validation.

Contribution

It introduces new bias correction methods for $$ estimators tailored for exponential distributions, enhancing multiple testing procedures with theoretical and empirical support.

Findings

Bias correction reduces estimator bias significantly.

Proposed estimators outperform existing methods in simulations.

Application to synthetic reliability data demonstrates practical utility.

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 exponentially distributed random observations 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. We also point out the adverse effect of using the model based bias correction method without proper assessment of the underlying distribution. A case-study is done with a synthetic dataset in connection with reliability and warranty studies to demonstrate the applicability of the procedure, under a non-Gaussian set up. 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.