# An approximate randomization test for the high-dimensional two-sample Behrens–Fisher problem under arbitrary covariances

@article{Wang2021AnAR, title={An approximate randomization test for the high-dimensional two-sample Behrens–Fisher problem under arbitrary covariances}, author={Rui Wang and Wangli Xu}, journal={Biometrika}, year={2021} }

This paper is concerned with the problem of comparing the population means of two groups of independent observations. An approximate randomization test procedure based on the test statistic of? is proposed. The asymptotic behaviour of the test statistic as well as the randomized statistic is studied under weak conditions. In our theoretical framework, observations are not assumed to be identically distributed even within groups. No condition on the eigenstructure of the covariance matrices is…

## 3 Citations

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

- Computer Science, MathematicsProceedings of the 4th International Conference on Statistics: Theory and Applications
- 2022

Here, a private non-parametric projection test is considered for the comparison of the high-dimensional multivariate mean vectors that guarantees strong differential privacy and gives accurate inference under the null hypothesis and a higher power under the local alternative hypothesis.

### Two-Sample Test for High-Dimensional Covariance Matrices: a normal-reference approach

- Mathematics
- 2022

,

### Nonparametric two-sample tests of high dimensional mean vectors via random integration

- MathematicsJournal of the American Statistical Association
- 2022

## References

SHOWING 1-10 OF 52 REFERENCES

### A Simple Two-Sample Test in High Dimensions Based on L2-Norm

- Mathematics, Computer ScienceJournal of the American Statistical Association
- 2019

An L2-norm based test that works under mild conditions and even when there are fewer observations than the dimension is proposed and can cope with singularity or near singularity of the covariance which is commonly seen in high dimensions and is the main cause of nonnormality.

### Two‐sample test of high dimensional means under dependence

- Mathematics
- 2014

A new test statistic is introduced that is based on a linear transformation of the data by the precision matrix which incorporates the correlations between the variables and is shown to be particularly powerful against sparse alternatives and enjoys certain optimality.

### Distribution and correlation-free two-sample test of high-dimensional means

- Mathematics, Computer ScienceThe Annals of Statistics
- 2020

This two-sample test based on a nontrivial extension of the one-sample central limit theorem provides a practically useful procedure with rigorous theoretical guarantees on its size and power assessment.

### Two-sample Behrens–Fisher problems for high-dimensional data: A normal reference approach

- Mathematics, Computer ScienceJournal of Statistical Planning and Inference
- 2021

### On the behaviour of randomization tests without the group invariance assumption

- Mathematics
- 1990

Abstract Fisher's randomization construction of hypothesis tests is a powerful tool to yield tests that are nonparametric in nature in that their level is exactly equal to the nominal level in finite…

### EXACT AND ASYMPTOTICALLY ROBUST PERMUTATION TESTS

- Mathematics
- 2013

Given independent samples from P and Q, two-sample permutation tests allow one to construct exact level tests when the null hypothesis is P=Q. On the other hand, when comparing or testing particular…

### EFFECT OF HIGH DIMENSION: BY AN EXAMPLE OF A TWO SAMPLE PROBLEM

- Mathematics
- 1999

With the rapid development of modern computing techniques, statisticians are dealing with data with much higher dimension. Consequently, due to their loss of accuracy or power, some classical…

### A Further Study on Chen–Qin’s Test for Two-Sample Behrens–Fisher Problems for High-Dimensional Data

- MathematicsJournal of Statistical Theory and Practice
- 2022

A further study on Chen–Qin’s test, namely CQ test, for two-sample Behrens–Fisher problems for high-dimensional data is conducted, resulting in a new normal-reference test where the null distribution…

### Randomization Tests Under an Approximate Symmetry Assumption

- Mathematics, Computer Science
- 2017

Conditions under which the same construction can be used to construct tests that asymptotically control the probability of a false rejection whenever the distribution of the observed data exhibits approximate symmetry in the sense that the limiting distribution of a function of the data exhibits symmetry under the null hypothesis are provided.

### TWO-SAMPLE BEHRENS-FISHER PROBLEM FOR HIGH-DIMENSIONAL DATA

- Mathematics
- 2015

This article is concerned with the two-sample Behrens-Fisher problem in high-dimensional settings. A novel test is proposed that is scale-invariant, asymp- totically normal under certain mild…