Symmetrical Independence Tests for Two Random Vectors with Arbitrary Dimensional Graphs

• 作者: Jia Min LIU Gao Rong LI Jian Qiang ZHANG Wang Li XU
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2022,（4）
• 页码范围: 662-682
• 页数: 21页
• 语种: 英文

摘要

Test of independence between random vectors X and Y is an essential task in statistical inference.One type of testing methods is based on the minimal spanning tree of variables X and Y.The main idea is to generate the minimal spanning tree for one random vector X,and for each edges in minimal spanning tree,the corresponding rank number can be calculated based on another random vector Y.The resulting test statistics are constructed by these rank numbers.However,the existed statistics are not symmetrical tests about the random vectors X and Y such that the power performance from minimal spanning tree of X is not the same as that from minimal spanning tree of Y.In addition,the conclusion from minimal spanning tree of X might conflict with that from minimal spanning tree of Y.In order to solve these problems,we propose several symmetrical independence tests for X and Y.The exact distributions of test statistics are investigated when the sample size is small.Also,we study the asymptotic properties of the statistics.A permutation method is introduced for getting critical values of the statistics.Compared with the existing methods,our proposed methods are more efficient demonstrated by numerical analysis.