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Statistica Sinica 25 (2015), 1297-1312

TWO-SAMPLE BEHRENS-FISHER PROBLEM
FOR HIGH-DIMENSIONAL DATA
Long Feng1, Changliang Zou1, Zhaojun Wang1 and Lixing Zhu2
1Nankai University and 2Hong Kong Baptist University

Abstract: This article is concerned with the two-sample Behrens-Fisher problem in high-dimensional settings. A test is proposed that is scale-invariant, asymptotically normal under certain mild conditions, and the dimensionality is allowed to grow in the rate, respectively, from square to cube of the sample size in different scenarios. We explain the necessity of bias correction for existing scale-invariant tests. We also give some examples to show the advantage of the scale-invariant test over scale-variant tests when variances of the two samples are different.

Key words and phrases: Asymptotic normality, Behrens-Fisher problem, high-dimensional data, large-p-small-n, two-sample test.

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