arXiv subjects

Luella Fu

Publications and source records attributed to Luella Fu.

4 recordsLinked to original sources

arXiv2024

False Discovery Control in Multiple Testing: A Brief Overview of Theories and Methodologies

As the volume and complexity of data continue to expand across various scientific disciplines, the need for robust methods to account for the multiplicity of comparisons has grown widespread. A popular measure of type 1 error rate in multiple testing literature is the false discovery rate (FDR). The FDR provides a powerful and practical approach to large-scale multiple testing and has been successfully used in a wide range of applications. The concept of FDR has gained wide acceptance in the statistical community and various methods has been proposed to control the FDR. In this work, we review the latest developments in FDR control methodologies. We also develop a conceptual framework to better describe this vast literature; understand its intuition and key ideas; and provide guidance for the researcher interested in both the application and development of the methodology.

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arXiv2023

Ranking and Selection in Large-Scale Inference of Heteroscedastic Units

The allocation of limited resources to a large number of potential candidates presents a pervasive challenge. In the context of ranking and selecting top candidates from heteroscedastic units, conventional methods often result in over-representations of subpopulations, and this issue is further exacerbated in large-scale settings where thousands of candidates are considered simultaneously. To address this challenge, we propose a new multiple comparison framework that incorporates a modified power notion to prioritize the selection of important effects and employs a novel ranking metric to assess the relative importance of units. We develop both oracle and data-driven algorithms, and demonstrate their effectiveness in controlling the error rates and achieving optimality. We evaluate the numerical performance of our proposed method using simulated and real data. The results show that our framework enables a more balanced selection of effects that are both statistically significant and practically important, and results in an objective and relevant ranking scheme that is well-suited to practical scenarios.

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arXiv2021

An Empirical Bayes Approach to Controlling the False Discovery Exceedance

In large-scale multiple hypothesis testing problems, the false discovery exceedance (FDX) provides a desirable alternative to the widely used false discovery rate (FDR) when the false discovery proportion (FDP) is highly variable. We develop an empirical Bayes approach to control the FDX. We show that, for independent hypotheses from a two-group model and dependent hypotheses from a Gaussian model fulfilling the exchangeability condition, an oracle decision rule based on ranking and thresholding the local false discovery rate (lfdr) is optimal in the sense that the power is maximized subject to the FDX constraint. We propose a data-driven FDX procedure that uses carefully designed computational shortcuts to emulate the oracle rule. We investigate the empirical performance of the proposed method using both simulated and real data and study the merits of FDX control through an application for identifying abnormal stock trading strategies.

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arXiv2020

Heterocedasticity-Adjusted Ranking and Thresholding for Large-Scale Multiple Testing

Standardization has been a widely adopted practice in multiple testing, for it takes into account the variability in sampling and makes the test statistics comparable across different study units. However, despite conventional wisdom to the contrary, we show that there can be a significant loss in information from basing hypothesis tests on standardized statistics rather than the full data. We develop a new class of heteroscedasticity--adjusted ranking and thresholding (HART) rules that aim to improve existing methods by simultaneously exploiting commonalities and adjusting heterogeneities among the study units. The main idea of HART is to bypass standardization by directly incorporating both the summary statistic and its variance into the testing procedure. A key message is that the variance structure of the alternative distribution, which is subsumed under standardized statistics, is highly informative and can be exploited to achieve higher power. The proposed HART procedure is shown to be asymptotically valid and optimal for false discovery rate (FDR) control. Our simulation results demonstrate that HART achieves substantial power gain over existing methods at the same FDR level. We illustrate the implementation through a microarray analysis of myeloma.

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