Two-sample Behrens–Fisher problems for high-dimensional data: a normal reference scale-invariant test

Zhang, Liang; Zhu, Tianming; Zhang, Jin‐Ting

doi:10.1080/02664763.2020.1834516

Cited by 4 publications

(1 citation statement)

References 14 publications

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“…Bai and Saranadasa (1996) [8] proposed a modification of the Hotelling statistic by using the -norm but not involving the inverse of the covariance matrix which is specified later. See also [1], [9]- [11]. However, the underlying distribution of many real data tends to be non-normal even after log transformation or can be not known.…”

Section: Introductionmentioning

confidence: 99%

Comparison Of Two Mean Vectors Under Differential Privacy For High-Dimensional Data

Huang¹,

Wang²,

Hu³

et al. 2022

Proceedings of the 4th International Conference on Statistics: Theory and Applications

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The multivariate hypothesis testing problem is a more interesting task of the statistical inference for high-dimensional data nowadays, in which the dimension of the observation vectors is diverging and could even be larger than the sample size. However, in many applications of multivariate hypotheses problems, the data are highly sensitive and require privacy protection. Here we consider a private non-parametric projection test for the comparison of the high-dimensional multivariate mean vectors that guarantees strong differential privacy. The empirical evidence shows that the non-parametric projection test under differential privacy gives accurate inference under the null hypothesis and a higher power under the local alternative hypothesis.

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Section: Introductionmentioning

confidence: 99%