Robust Permutation Tests For Correlation And Regression Coefficients
研究了双变量样本独立性检验中置换检验的缺陷，提出学生化样本相关系数的置换检验方法，能精确控制第一类错误率，并推广到回归系数的稳健置换检验。
Given a sample from a bivariate distribution, consider the problem of testing independence. A permutation test based on the sample correlation is known to be an exact level α test. However, when used to test the null hypothesis that the samples are uncorrelated, the permutation test can have rejection probability that is far from the nominal level. Further, the permutation test can have a large Type 3 (directional) error rate, whereby there can be a large probability that the permutation test rejects because the sample correlation is a large positive value, when in fact the true correlation is negative. It will be shown that studentizing the sample correlation leads to a permutation test which is exact under independence and asymptotically controls the probability of Type 1 (or Type 3) errors. These conclusions are based on our results describing the almost sure limiting behavior of the randomization distribution. We will also present asymptotically robust randomization tests for regression coefficients, including a result based on a modified procedure of Freedman and Lane. Simulations and empirical applications are included. Supplementary materials for this article are available online.