Open Access
2024 Sparse-limit approximation for t-statistics
Micól Tresoldi, Daniel Xiang, Peter McCullagh
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Electron. J. Statist. 18(1): 1586-1602 (2024). DOI: 10.1214/24-EJS2238


In a range of genomic applications, it is of interest to quantify the evidence that the signal at site i is active given conditionally independent replicate observations summarized by the sample mean and variance (Y¯,s2) at each site. We study the version of the problem in which the signal distribution is sparse, and the error distribution has an unknown site-specific variance so that the null distribution of the standardized statistic is Student-t rather than Gaussian. The main contribution of this paper is a sparse-mixture approximation to the non-null density of the t-ratio. This formula demonstrates the effect of low degrees of freedom on the Bayes factor, or the conditional probability that the site is active. We illustrate some differences on a HIV dataset for gene-expression data.


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Micól Tresoldi. Daniel Xiang. Peter McCullagh. "Sparse-limit approximation for t-statistics." Electron. J. Statist. 18 (1) 1586 - 1602, 2024.


Received: 1 December 2023; Published: 2024
First available in Project Euclid: 28 March 2024

Digital Object Identifier: 10.1214/24-EJS2238

Vol.18 • No. 1 • 2024
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