在未知对称零假设下估计局部错误发现率
Estimating the local false discovery rate under an unknown symmetric null
AI总结：
针对零分布仅对称于零的双组模型，提出基于逻辑回归和自然三次样条的局部错误发现率估计方法，并证明该估计可渐近控制多重检验的局部错误发现率。
摘要：
本文关注在双组模型中估计局部错误发现率（lfdr），其中关于零分布的唯一假设是它关于零对称。我们的动机来自当代多重假设检验框架，特别适用于变量选择问题，该框架将任何用户指定的分数转换为统计量，其零分布关于零对称，而非零分布通常预期在零右侧富集。虽然现代方法如knockoff滤波器（Barber and Candes; 2015）能够利用零性质来控制错误发现率（FDR），但一个更合适的目标是针对被拒绝的假设控制局部错误发现率，如Soloff等人（2024）所提出的，其中分析了标准的双组模型（已知$f_0$和独立性）。在这里，我们朝这个方向迈出一步，提出通过针对替代密度比$f(-w)/f(w)$（$w>0$）来估计lfdr，其中$f$是上述“简化”双组模型中的边际密度。我们研究了几种估计量，并提出了一种基于自然三次样条基的逻辑回归方法。我们还证明了该替代的任何一致估计量都能使以名义水平阈值估计的多重检验过程渐近控制lfdr。
英文摘要：
This paper is concerned with estimating the local false discovery rate (lfdr) in a two-groups model where the only assumption regarding the null distribution is symmetry about zero. Our motivation comes from the contemporary framework for multiple hypothesis testing, particularly relevant in variable selection problems, which transforms any user-specified scores into statistics whose null distributions are symmetric about zero, whereas enrichment to the right of zero is generally expected for the non-nulls. While modern methods such as the knockoff filter (Barber and Candes; 2015) are able to exploit the null property for controlling the false discovery rate (FDR), an arguably more appropriate goal is to target control of the local false discovery rate for the rejected hypotheses, as proposed in Soloff et al. (2024) where the standard two-groups model (known $f_0$ and independence) is analyzed. Here, we take a step in this direction and propose to estimate the lfdr by targeting the surrogate density ratio $f(-w)/f(w)$, for $w>0$, where $f$ is the marginal density in the aforementioned ``stripped-down'' two-groups model. We study several estimators and propose a logistic regression based method with natural cubic spline basis. We also show that any consistent estimator of this surrogate yields asymptotic lfdr control of the multiple testing procedure that thresholds the estimate at the nominal level.
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