A Class of Permutation Tests of Bivariate Interchangeability
提出一类精确且无分布假设的置换检验，用于同时检测双变量数据中边际位置和/或尺度的差异，通过模拟证明其优于标准检验。
Abstract A set of permutation tests that are both exact and distribution-free are proposed to simultaneously detect differences in marginal locations and/or scales in bivariate data. The tests take advantage of the fact that when the marginal means and variances are equal, the pairwise differences are symmetrically distributed about 0 and are uncorrelated with the pairwise sums. Two statistics for detecting the marginal location and scale differences are combined in a quadratic form. A permutation distribution for this quadratic form follows from considering all 2 n conditionally equally likely sign changes on the differences. Several methods of estimating the covariance matrix of the quadratic form are examined, including conditional and unconditional (plug-in) approaches. These new tests are compared with the standard tests in the literature and, through simulation for several families of bivariate distributions, are found to compare quite favorably. This article also brings to light the largely overlooked likelihood ratio test for equal means and variances in the bivariate normal and shows its relationship to more recent approaches, including those presented here.