arXiv subjects

Deepra Ghosh

Publications and source records attributed to Deepra Ghosh.

3 recordsLinked to original sources

arXiv2026

Global Testing of Gaussian Means by Combining Marginal and Conditional Evidence

We propose a test of the global null hypothesis of zero means in correlated multivariate Gaussian data by combining marginal and conditional evidence at each coordinate. The conditional tests are based on the distribution of each coordinate given the remaining coordinates. At each coordinate, the corresponding two-sided $p$-values are combined using the Simes method, followed by a Bonferroni correction across coordinates. Because conditioning can either strengthen or weaken evidence against the null, neither marginal nor conditional testing is uniformly preferable. The proposed procedure adapts to their relative strengths while retaining the simplicity of minimum-type global testing. We establish finite-sample control of the global Type-I error under both known covariance and covariance estimated from an independent sample. The latter setting requires a careful analysis of the dependence between studentized marginal and conditional statistics. We evaluate the power of the proposed test through simulations, compare its performance with existing global tests, and illustrate its practical utility using a TCGA carcinoma dataset.

stat.ME↗

arXiv2026

Further Results on Controlling the False Discovery Rate in Two-Sided Gaussian Mean Testing

The recent work of Sarkar and Zhang (2025) introduced Positive Tail Dependence Under the Null (PTDN) and developed Generalized Shifted Benjamini-Hochberg (BH) procedures for two-sided Gaussian $z$- and $t$-testing under known covariance structures. This paper develops further consequences of that framework. First, we derive explicit dependence-adaptive lower and upper bounds for the FDR of the original BH procedure in terms of the conditional variance parameters $τ_i=1-R_i^2$, where $R_i^2$ is the squared multiple correlation between the $i$th statistic and the remaining coordinates. These bounds recover the exact BH FDR under independence and provide finite-sample, covariance-specific information complementary to generic bounds. We also identify conditions under which the coordinate-specific calibration of shifted BH can provide a rejection advantage over the original BH procedure. Second, we consider the practically important setting in which the covariance matrix is unknown but an independent Wishart estimator is available. Using simultaneous lower confidence bounds for the $τ_i$'s, we construct a confidence-bound shifted BH procedure and establish finite-sample FDR control. To our knowledge, this is the first shifted-BH-type procedure with a finite-sample guarantee for two-sided Gaussian mean testing under a completely unknown covariance matrix estimated independently. Numerical studies illustrate the behavior of the covariance-adaptive bounds, the potential advantage of shifted BH over BH, and the performance of confidence-bound shifting under unknown covariance.

stat.ME↗

arXiv2025

Dependence-Aware False Discovery Rate Control in Two-Sided Gaussian Mean Testing

This paper develops a general framework for controlling the false discovery rate (FDR) in multiple testing of Gaussian means against two-sided alternatives. The widely used Benjamini-Hochberg (BH) procedure provides exact FDR control under independence or conservative control under specific one-sided dependence structures, but its validity for correlated two-sided tests has remained an open question. We introduce the notion of positive left-tail dependence under the null (PLTDN), extending classical dependence assumptions to two-sided settings, and show that it ensures valid FDR control for BH-type procedures. Building on this framework, we propose a family of generalized shifted BH (GSBH) methods that incorporate correlation information through simple p-value adjustments. Simulation results demonstrate reliable FDR control and improved power across a range of dependence structures, while an application to an HIV gene expression dataset illustrates the practical effectiveness of the proposed approach.

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