Two-sample Behrens-Fisher problem for high-dimensional data

Long Feng; Changliang Zou; Zhaojun Wang; Lixing ZHU

doi:10.5705/ss.2014.048

Two-sample Behrens-Fisher problem for high-dimensional data

Long Feng, Changliang Zou, Zhaojun Wang, Lixing ZHU^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

42 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1297-1312
Number of pages	16
Journal	Statistica Sinica
Volume	25
Issue number	4
DOIs	https://doi.org/10.5705/ss.2014.048
Publication status	Published - Oct 2015

Scopus Subject Areas

Statistics and Probability
Statistics, Probability and Uncertainty

User-Defined Keywords

Asymptotic normality
Behrens-Fisher problem
High-dimensional data
Large-p-small-n
Two-sample test

Access to Document

10.5705/ss.2014.048

http://www3.stat.sinica.edu.tw/statistica/oldpdf/A25n41.pdf

Cite this

@article{39c41a50576a424cb01b5f096d56739c,

title = "Two-sample Behrens-Fisher problem for high-dimensional data",

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.",

keywords = "Asymptotic normality, Behrens-Fisher problem, High-dimensional data, Large-p-small-n, Two-sample test",

author = "Long Feng and Changliang Zou and Zhaojun Wang and Lixing ZHU",

note = "Funding Information: The authors thank the Editor, an associate editor, and two referees for their many helpful comments that have resulted in significant improvements in the article. Feng and Zhu were partly supported by a grant from the Research Grants Council of Hong Kong, Hong Kong, China. Zou and Wang was supported by the NNSF of China Grants 11431006, 11131002, 11371202, 11471069, the Foundation for the Author of National Excellent Doctoral Dissertation of PR China 201232.",

year = "2015",

month = oct,

doi = "10.5705/ss.2014.048",

language = "English",

volume = "25",

pages = "1297--1312",

journal = "Statistica Sinica",

issn = "1017-0405",

publisher = "Institute of Statistical Science",

number = "4",

}

TY - JOUR

T1 - Two-sample Behrens-Fisher problem for high-dimensional data

AU - Feng, Long

AU - Zou, Changliang

AU - Wang, Zhaojun

AU - ZHU, Lixing

N1 - Funding Information: The authors thank the Editor, an associate editor, and two referees for their many helpful comments that have resulted in significant improvements in the article. Feng and Zhu were partly supported by a grant from the Research Grants Council of Hong Kong, Hong Kong, China. Zou and Wang was supported by the NNSF of China Grants 11431006, 11131002, 11371202, 11471069, the Foundation for the Author of National Excellent Doctoral Dissertation of PR China 201232.

PY - 2015/10

Y1 - 2015/10

N2 - 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.

AB - 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.

KW - Asymptotic normality

KW - Behrens-Fisher problem

KW - High-dimensional data

KW - Large-p-small-n

KW - Two-sample test

UR - http://www3.stat.sinica.edu.tw/statistica/J25N4/J25N41/J25N41.html

UR - https://www.jstor.org/stable/24721234

UR - http://www.scopus.com/inward/record.url?scp=84994868514&partnerID=8YFLogxK

U2 - 10.5705/ss.2014.048

DO - 10.5705/ss.2014.048

M3 - Journal article

AN - SCOPUS:84994868514

SN - 1017-0405

VL - 25

SP - 1297

EP - 1312

JO - Statistica Sinica

JF - Statistica Sinica

IS - 4

ER -

Two-sample Behrens-Fisher problem for high-dimensional data

Abstract

Scopus Subject Areas

User-Defined Keywords

Access to Document

Other files and links

Fingerprint

Cite this