基于符号秩的高维均值检验

Signed-rank-based test for high dimensional mean vector

研究高维情形下一样本均值检验的问题。已有的一些高维均值检验方法假设样本具有椭球等高分布。为应用到更多的分布,提出基于符号秩的均值检验统计量。所提方法是稳健的且具有刻度变换不变性。建立了所提出检验统计量的渐近性质,数值模拟表明该方法可以很好地控制第一类错误,且功效更高。还将该方法应用到眼科数据中。

This work is concerned with tests for one-sample mean vectors under high dimensional cases.Existing high dimensional tests for mean vectors base on the assumption of elliptical distribution have been proposed recently.To extend to more distributions,we propose a signed-rankbased test.The proposed test statistic is robust and scalar-invariant.Asymptotic properties of the test statistic are established.Numerical studies show that the proposed test has a good control of the type-I error and is more efficiency.We also employ the proposed method to analyze an ophthalmic data.