Sample‐size calculation for tests of homogeneity. Issue 1 (18th January 2016)

• Record Type: Journal Article
• Authors: Chen, Jiahua; Li, Pengfei; Liu, Yukun
• Is Part Of: Canadian journal of statistics. Volume 44:Issue 1(2016)
• Page Start: 82
• Page End: 101
• Publication Date: 2016-01-18
• Subjects: Calibration -- C(α) test -- contiguity theory -- EM‐test -- exponential family -- homogeneity -- local alternative -- locally most powerful test -- mixture model -- MSC 2010: Primary 62P99 -- 62P10 -- secondary 62F03; Mathematical statistics -- Periodicals; 519.5
• DOI: 10.1002/cjs.11274
• Languages: English
• ISSNs: 0319-5724

Abstract

Abstract: Mixture models are widely used to explain excessive variation in observations that is not captured by standard parametric models, and they lead to suggestive latent structures. The hypothetical latent structure often needs critical examination based on experimental data. It is therefore important to know the sample size needed to ensure a reasonable chance of success. We investigate this issue for the EM‐test and the C ( α ) test. They are shown to be asymptotically equivalent and have simple limiting distributions under two sets of local alternatives for commonly used mixture models. We obtain a simple sample‐size formula and an associated simulation‐based calibration procedure, and we demonstrate via data examples and simulation studies that they provide useful guidance for several common mixture models. The Canadian Journal of Statistics 44: 82–101; 2016 © 2016 Statistical Society of Canada