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<p>The estimation of the number of null hypotheses is closely related to error rate control process such as the Family-Wise Error Rate (FWER) and the False Discovery Rate (FDR), in multiple hypothesis testing problems. Several methods have been proposed to address this challenge, including the <i>p</i> value graph type methods. In this paper, we introduce a novel <i>p</i> value graph type method for estimating the number of true null hypotheses. Our method constructs a mean-change point model using the differences of the adjacent order <i>p</i> values, and applies the CUSUM statistic to detect potential change point. Based on the change point detection result, the number of true null hypotheses is estimated. Various simulation studies and a real data application are conducted with comparison to other existing methods. The numerical results demonstrate that the new estimating method is robust and achieves superior performance across various scenarios. It is versatile and can handle diverse settings, including cases where all hypotheses are null, all are alternative, or only a subset are null hypotheses.</p>

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Estimating the number of true null hypotheses based on change point of observed p values

  • 期刊论文

  • 发表日期：

    2025年5月16日

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  • Lishuai Jin,
  • Hongyan Fang,
  • Wenzhi Yang

摘要

The estimation of the number of null hypotheses is closely related to error rate control process such as the Family-Wise Error Rate (FWER) and the False Discovery Rate (FDR), in multiple hypothesis testing problems. Several methods have been proposed to address this challenge, including the p value graph type methods. In this paper, we introduce a novel p value graph type method for estimating the number of true null hypotheses. Our method constructs a mean-change point model using the differences of the adjacent order p values, and applies the CUSUM statistic to detect potential change point. Based on the change point detection result, the number of true null hypotheses is estimated. Various simulation studies and a real data application are conducted with comparison to other existing methods. The numerical results demonstrate that the new estimating method is robust and achieves superior performance across various scenarios. It is versatile and can handle diverse settings, including cases where all hypotheses are null, all are alternative, or only a subset are null hypotheses.