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Sign-based test for mean vector in high-dimensional and sparse settings. (English) Zbl 1435.62200
From the authors’ abstract: “In this article, we introduce a robust sparse test statistic which is based on the maximum type statistic. Both the limiting null distribution of the test statistic and the power of the test are analysed.”
Through numerical simulations, the performance of the proposed test is compared with the performance of other tests available in the literature. The authors show that the proposed test outperforms other tests in the case of sparse alternative. In fact, the numerical results presented in the paper concern alternatives where only a small fraction of means are different from zero. For $$p=50,100$$ or $$200$$ variables, the number of non-zero means in the alternative hypothesis is $$[\sqrt{p}]$$ or $$[0.05p]$$, where $$[x ]$$ is the floor of the real number $$x$$. In both cases and for different distributions, the power of the proposed test is higher than the power of the other tests, especially for the largest value of $$p$$, i.e., $$p=200$$.

##### MSC:
 62H15 Hypothesis testing in multivariate analysis 62R07 Statistical aspects of big data and data science 62G35 Nonparametric robustness
QRM
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