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The likelihood ratio test for simple tree order: A useful asymptotic expansion
Institution:1. Department of Mathematics, Beijing Jiao Tong University, Beijing 100044, China;2. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, China;3. Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia;4. School of Mathematics, South China University of Technology, Guangzhou 510640, China;5. Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA;6. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China;7. International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa;1. Department of Mathematics, Ohio University, Athens, Ohio, USA;2. Department of Mathematics, Lafayette College, Easton, Pennsylvania, USA
Abstract:We derive new approximations for the likelihood ratio statistics that are used in testing hypotheses involving simple tree order. They are based on asymptotics when the number of populations tends to infinity and variances are equal.As an application quantiles are obtained that are much easier to calculate than exact critical values or the gamma-approximation usually proposed in literature. Our quantitles also provide often better approximations than those known in literature.
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