The sparse variance contamination model. Issue 5 (2nd September 2020)

• Record Type: Journal Article
• Authors: Arias-Castro, Ery; Huang, Rong
• Is Part Of: Statistics. Volume 54:Issue 5(2020)
• Page Start: 1081
• Page End: 1093
• Publication Date: 2020-09-02
• Subjects: Gaussian mixtures -- change in variance -- likelihood ratio test -- higher criticism test; 62F03 -- 62F05; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2020.1823394
• Languages: English
• ISSNs: 0233-1888

Abstract

Abstract : We consider a Gaussian contamination (i.e., mixture) model where the contamination manifests itself as a change in variance. We study this model in various asymptotic regimes, in parallel with the work of Ingster YI. [Some problems of hypothesis testing leading to infinitely divisible distributions. Math Methods Stat. 1997;6(1):47–69] and Donoho D, Jin J. [Higher criticism for detecting sparse heterogeneous mixtures. Ann Stat. 2004;32(3):962–994], who considered a similar model where the contamination was in the mean instead. We show that the higher criticism test is (first-order) comparable to the likelihood ratio test in all sparsity regimes, while the chi-squared test and the extremes test are suboptimal.