【主讲】Wenxin Zhou (Princeton University)
【主题】FARM-Test: Factor-Adjusted Robust Multiple Testing with False Discovery Control
【时间】2017年6月1日 (周四) 15：30-17：00
【地点】上海财经大学经济学院楼402室
【语言】英文
【摘要】Heavy-tailed distributions arise easily from high-dimensional data and they are at odd with the commonly used sub-Gaussian assumptions. This prompts us to revisit the Huber estimator from a new perspective. The key observation is that the robustification parameter should adapt to the sample size, dimension and moments for an optimal bias-robustness tradeoff: a small robustification parameter increases the robustness of estimation but introduces more biases. Our framework is able to handle heavy-tailed data with bounded (1+δ)-th moment for any δ > 0. When δ = 1, we prove a sub-Gaussian deviation bound for the adaptive Huber estimator, and derive a nonasymptotic Bahadur representation which is useful to study the asymptotic properties of many estimators simultaneously.Based on the idea of robust estimation and inference, we propose a new factor-adjusted robust multiple testing procedure, named FARM-Test, to deal with the large-scale multiple testing problem with heavy-tailed and dependent data, in which the dependency is characterized by a few latent factors. The consistency of the our robust FDP estimators are investigated. Simulation studies further demonstrate the satisfactory finite sample performance of the FARM-Test.