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1. A new p-value based multiple testing procedure for generalized linear models

   https://doi.org/10.1007/s11222-025-10600-2  

   Rilling, Joseph; Tang, Cheng_Yong (March 2025, Statistics and Computing)

   Abstract This study introduces a novelp-value-based multiple testing approach tailored for generalized linear models. Despite the crucial role of generalized linear models in statistics, existing methodologies face obstacles arising from the heterogeneous variance of response variables and complex dependencies among estimated parameters. Our aim is to address the challenge of controlling the false discovery rate (FDR) amidst arbitrarily dependent test statistics. Through the development of efficient computational algorithms, we present a versatile statistical framework for multiple testing. The proposed framework accommodates a range of tools developed for constructing a new model matrix in regression-type analysis, including random row permutations and Model-X knockoffs. We devise efficient computing techniques to solve the encountered non-trivial quadratic matrix equations, enabling the construction of pairedp-values suitable for the two-step multiple testing procedure proposed by Sarkar and Tang (Biometrika 109(4): 1149–1155, 2022). Theoretical analysis affirms the properties of our approach, demonstrating its capability to control the FDR at a given level. Empirical evaluations further substantiate its promising performance across diverse simulation settings. 

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2. Multi-scale Fisher’s independence test for multivariate dependence

   https://doi.org/10.1093/biomet/asac013  

   Gorsky, S; Ma, L (February 2022, Biometrika)

   Summary Identifying dependency in multivariate data is a common inference task that arises in numerous applications. However, existing nonparametric independence tests typically require computation that scales at least quadratically with the sample size, making it difficult to apply them in the presence of massive sample sizes. Moreover, resampling is usually necessary to evaluate the statistical significance of the resulting test statistics at finite sample sizes, further worsening the computational burden. We introduce a scalable, resampling-free approach to testing the independence between two random vectors by breaking down the task into simple univariate tests of independence on a collection of $$2\times 2$$ contingency tables constructed through sequential coarse-to-fine discretization of the sample , transforming the inference task into a multiple testing problem that can be completed with almost linear complexity with respect to the sample size. To address increasing dimensionality, we introduce a coarse-to-fine sequential adaptive procedure that exploits the spatial features of dependency structures. We derive a finite-sample theory that guarantees the inferential validity of our adaptive procedure at any given sample size. We show that our approach can achieve strong control of the level of the testing procedure at any sample size without resampling or asymptotic approximation and establish its large-sample consistency. We demonstrate through an extensive simulation study its substantial computational advantage in comparison to existing approaches while achieving robust statistical power under various dependency scenarios, and illustrate how its divide-and-conquer nature can be exploited to not just test independence, but to learn the nature of the underlying dependency. Finally, we demonstrate the use of our method through analysing a dataset from a flow cytometry experiment. 

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3. Differentially private false discovery rate control

   https://doi.org/10.29012/jpc.755  

   Dwork, Cynthia; Su, Weijie; Zhang, Li (September 2021, Journal of Privacy and Confidentiality)

   Differential privacy provides a rigorous framework for privacy-preserving data analysis. This paper proposes the first differentially private procedure for controlling the false discovery rate (FDR) in multiple hypothesis testing. Inspired by the Benjamini-Hochberg procedure (BHq), our approach is to first repeatedly add noise to the logarithms of the p-values to ensure differential privacy and to select an approximately smallest p-value serving as a promising candidate at each iteration; the selected p-values are further supplied to the BHq and our private procedure releases only the rejected ones. Moreover, we develop a new technique that is based on a backward submartingale for proving FDR control of a broad class of multiple testing procedures, including our private procedure, and both the BHq step- up and step-down procedures. As a novel aspect, the proof works for arbitrary dependence between the true null and false null test statistics, while FDR control is maintained up to a small multiplicative factor. 

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4. A New Robustness Metric for Robust Design Optimization Under Time- and Space-Dependent Uncertainty Through Metamodeling

   https://doi.org/https://doi.org/10.1115/DETC2019-97611  

   Xinpeng Wei, Xiaoping Du (January 2019, the ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference)

   Product performance varies with respect to time and space in many engineering applications. This work discusses how to measure and evaluate the robustness of a product or component when its quality characteristics are functions of random variables, random fields, temporal variables, and spatial variables. At first, the existing time-dependent robustness metric is extended to the present time- and space-dependent problem. The robustness metric is derived using the extreme value of the quality characteristics with respect to temporal and spatial variables for the nominal-the-better type quality characteristics. Then a metamodel-based numerical procedure is developed to evaluate the new robustness metric. The procedure employs a Gaussian Process regression method to estimate the expected quality loss that involves the extreme quality characteristics. The expected quality loss is obtained directly during the regression model building process. Three examples are used to demonstrate the robustness analysis method. The proposed method can be used for robustness assessment during robust design optimization under time- and space-dependent uncertainty. 

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5. Compositional knockoff filter for high‐dimensional regression analysis of microbiome data

   https://doi.org/10.1111/biom.13336  

   Srinivasan, Arun; Xue, Lingzhou; Zhan, Xiang (July 2020, Biometrics)

   Abstract A critical task in microbiome data analysis is to explore the association between a scalar response of interest and a large number of microbial taxa that are summarized as compositional data at different taxonomic levels. Motivated by fine‐mapping of the microbiome, we propose a two‐step compositional knockoff filter to provide the effective finite‐sample false discovery rate (FDR) control in high‐dimensional linear log‐contrast regression analysis of microbiome compositional data. In the first step, we propose a new compositional screening procedure to remove insignificant microbial taxa while retaining the essential sum‐to‐zero constraint. In the second step, we extend the knockoff filter to identify the significant microbial taxa in the sparse regression model for compositional data. Thereby, a subset of the microbes is selected from the high‐dimensional microbial taxa as related to the response under a prespecified FDR threshold. We study the theoretical properties of the proposed two‐step procedure, including both sure screening and effective false discovery control. We demonstrate these properties in numerical simulation studies to compare our methods to some existing ones and show power gain of the new method while controlling the nominal FDR. The potential usefulness of the proposed method is also illustrated with application to an inflammatory bowel disease data set to identify microbial taxa that influence host gene expressions. 

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