@article{9aa4f988c085407b8ec360450dbc4f34,
title = "Regularized t distribution: definition, properties and applications",
abstract = "For gene expression data analysis, an important task is to identify genes that are differentially expressed between two or more groups. Nevertheless, as biological experiments are often measured with a relatively small number of samples, how to accurately estimate the variances of gene expression becomes a challenging issue. To tackle this problem, we introduce a regularized t distribution and derive its statistical properties including the probability density function and the moment generating function. The noncentral regularized t distribution is also introduced for computing the statistical power of hypothesis testing. For practical applications, we apply the regularized t distribution to establish the null distribution of the regularized t statistic, and then formulate it as a regularized t-test for detecting the differentially expressed genes. Simulation studies and real data analysis show that our regularized t-test performs much better than the Bayesian t-test in the “limma” package, in particular when the sample sizes are small.",
keywords = "Bayesian t-test, hypothesis testing, noncentral regularized t distribution, regularized t distribution, regularized t-test",
author = "Zongliang Hu and Yiping Yang and Gaorong Li and Tiejun Tong",
note = "Funding Information: The authors sincerely thank the editor, the associate editor, and one reviewer for their constructive comments that have led to a substantial improvement of this paper. Zongliang Hu's research was supported by National Natural Science Foundation of China (12001378), Guangdong Basic and Applied Basic Research Foundation (2019A1515110449), and Natural Science Foundation of Guangdong Province (2023A1515010027). Yiping Yang's research was supported by Chongqing Natural Science Foundation (cstc2021jcyj-msxmX0079) and Humanities and Social Sciences Program of Chongqing Education Commission (21SIGH118). Gaorong Li's research was supported by National Natural Science Foundation of China (12271046, 11871001, and 12131006). Tiejun Tong's research was supported by General Research Fund of Hong Kong (HKBU12303918 and HKBU12303421), Initiation Grant for Faculty Niche Research Areas (RC-FNRA-IG/20-21/SCI/03) of Hong Kong Baptist University, and National Natural Science Foundation of China (1207010822). Publisher Copyright: {\textcopyright} 2023 The Authors. Scandinavian Journal of Statistics published by John Wiley & Sons Ltd on behalf of The Board of the Foundation of the Scandinavian Journal of Statistics.",
year = "2023",
month = dec,
doi = "10.1111/sjos.12655",
language = "English",
volume = "50",
pages = "1884--1900",
journal = "Scandinavian Journal of Statistics",
issn = "0303-6898",
publisher = "Wiley-Blackwell Publishing Ltd",
number = "4",
}