Each week, we publish layman’s abstracts of new articles from our prestigious portfolio of journals in statistics. The aim is to highlight the latest research to a broader audience in an accessible format.
The article featured today is from the Canadian Journal of Statistics, with the full article now available to read here.
Sang, Y., Dang, X. and Zhao, Y. (2021), A Jackknife empirical likelihood approach for K-sample Tests. Can J Statistics. https://doi.org/10.1002/cjs.11611
Testing the equality of K distributions from independent random samples is a classical statistical problem encountered in almost every research field. Due to its fundamental importance and wide application, research for the K-sample problem has been kept active since the 1940s. Various tests have been proposed and new tests continue to emerge. In this paper, a new omnibus procedure is developed, indicating that the proposed test is against any general alternatives and is capable of detecting any departures from the equality of the K-distributions. As a nonparametric approach, jackknife empirical likelihood (JEL) is applied. It only assumes first moment without other restrictive assumptions on distributions of data. On the other hand, the test is effective with high powers, especially for the well-known Behrens-Fisher problem. The proposed JEL test works for univariate data as well as multivariate data. More specifically, the K-sample testing problem is transferred to the independence test between the numerical variable and the group label variable indicating samples from different populations. The test is based on the recently proposed Gini correlation which can characterize the independence. Numerical studies demonstrate that the proposed JEL test has satisfactory performance under a variety of situations. R code of the test is provided as the supplement to the paper.