Testing equality of a large number of densities

• 成果类型: Article
• 署名作者: Zhan, D.; Hart, J. D.
• 署名单位: Texas A&M University System; Texas A&M University College Station; Texas A&M University System; Texas A&M University College Station; Texas A&M University System; Texas A&M University College Station
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asu002
• 发表日期: 2014
• 页码: 449464
• 关键词: GOODNESS-OF-FIT; Small samples; statistics; components

摘要

The problem of testing equality of a large number of densities is considered. The classical k-sample problem compares a small, fixed number of distributions and allows the sample size from each distribution to increase without bound. In our asymptotic analysis the number of distributions tends to infinity but the size of individual samples remains fixed. The proposed test statistic is motivated by the simple idea of comparing kernel density estimators from the various samples to the average of all density estimators. However, a novel interpretation of this familiar type of statistic arises upon centring it. The asymptotic distribution of the statistic under the null hypothesis of equal densities is derived, and power against local alternatives is considered. It is shown that a consistent test is attainable in many situations where all but a vanishingly small proportion of densities are equal to each other. The test is studied via simulation, and an illustration involving microarray data is provided.