目前在文献中有很多关于多响应比较的研究方法，但是对带协变量调整的非参数检验的研究较少。一种直观的想法是将数据先投影到协变量的正交空间中，然后再利用秩和检验、调整的秩和检验或最大值检验方法。但是，功效普遍不高。在调整的秩和检验和伪F检验两种方法基础上，构建MIN2检验。大量模拟和实际数据表明，MIN2检验的效果优于现有的非参数检验方法。
Although there are many procedures developed for handling multiple outcomes comparison in the literature, the nonparametric methodology for group comparison with covariate adjustment is still in its infancy. One can use rank-sum test, adjusted rank-sum test, or max-type test by analyzing the processed data orthogonal to the space spanned by covariates. However, the power is not satisfactory. In this work, we combine the adjusted rank-sum test and pseudo F test and then construct a MIN2 test to handle this issue. The performances of MIN2 are thoroughly explored by extensive computer simulations and a real example.
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