Rank tests in heteroscedastic multi-way HANOVA

Haiyan Wang, Michael G. Akritas

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

This article develops rank tests for the nonparametric main factor effects and interactions in multi-way high-dimensional analysis of variance when the cell distributions are completely unspecified. The design can be balanced or unbalanced with the cell sample sizes fixed or tending to infinity. An arbitrary number of factors and all types of ordinal data are allowed. This extends the use of rank methods to the Neymann-Scott and triangular array problems. The asymptotic distribution of the rank statistics is obtained by showing their asymptotic equivalence to corresponding expressions based on the asymptotic rank transform. Compared with test procedures based on the original observations, the proposed rank procedures are free of moment conditions, converge to their limiting distribution faster, and have better power when the underlying distributions are heavy tailed or skewed. These advantages are demonstrated by simulations and an application to a real data set.

Original languageEnglish (US)
Pages (from-to)663-681
Number of pages19
JournalJournal of Nonparametric Statistics
Volume21
Issue number6
DOIs
StatePublished - Aug 1 2009

Fingerprint

Rank Test
Rank Statistics
Asymptotic Equivalence
Triangular Array
Ordinal Data
Cell Size
Moment Conditions
Dimensional Analysis
Analysis of variance
Limiting Distribution
Asymptotic distribution
Sample Size
High-dimensional
Infinity
Transform
Converge
Cell
Arbitrary
Interaction
Rank test

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

@article{cf6ac4c2c90c40d79b4c09000179a520,
title = "Rank tests in heteroscedastic multi-way HANOVA",
abstract = "This article develops rank tests for the nonparametric main factor effects and interactions in multi-way high-dimensional analysis of variance when the cell distributions are completely unspecified. The design can be balanced or unbalanced with the cell sample sizes fixed or tending to infinity. An arbitrary number of factors and all types of ordinal data are allowed. This extends the use of rank methods to the Neymann-Scott and triangular array problems. The asymptotic distribution of the rank statistics is obtained by showing their asymptotic equivalence to corresponding expressions based on the asymptotic rank transform. Compared with test procedures based on the original observations, the proposed rank procedures are free of moment conditions, converge to their limiting distribution faster, and have better power when the underlying distributions are heavy tailed or skewed. These advantages are demonstrated by simulations and an application to a real data set.",
author = "Haiyan Wang and Akritas, {Michael G.}",
year = "2009",
month = "8",
day = "1",
doi = "10.1080/10485250902971757",
language = "English (US)",
volume = "21",
pages = "663--681",
journal = "Journal of Nonparametric Statistics",
issn = "1048-5252",
publisher = "Taylor and Francis Ltd.",
number = "6",

}

Rank tests in heteroscedastic multi-way HANOVA. / Wang, Haiyan; Akritas, Michael G.

In: Journal of Nonparametric Statistics, Vol. 21, No. 6, 01.08.2009, p. 663-681.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Rank tests in heteroscedastic multi-way HANOVA

AU - Wang, Haiyan

AU - Akritas, Michael G.

PY - 2009/8/1

Y1 - 2009/8/1

N2 - This article develops rank tests for the nonparametric main factor effects and interactions in multi-way high-dimensional analysis of variance when the cell distributions are completely unspecified. The design can be balanced or unbalanced with the cell sample sizes fixed or tending to infinity. An arbitrary number of factors and all types of ordinal data are allowed. This extends the use of rank methods to the Neymann-Scott and triangular array problems. The asymptotic distribution of the rank statistics is obtained by showing their asymptotic equivalence to corresponding expressions based on the asymptotic rank transform. Compared with test procedures based on the original observations, the proposed rank procedures are free of moment conditions, converge to their limiting distribution faster, and have better power when the underlying distributions are heavy tailed or skewed. These advantages are demonstrated by simulations and an application to a real data set.

AB - This article develops rank tests for the nonparametric main factor effects and interactions in multi-way high-dimensional analysis of variance when the cell distributions are completely unspecified. The design can be balanced or unbalanced with the cell sample sizes fixed or tending to infinity. An arbitrary number of factors and all types of ordinal data are allowed. This extends the use of rank methods to the Neymann-Scott and triangular array problems. The asymptotic distribution of the rank statistics is obtained by showing their asymptotic equivalence to corresponding expressions based on the asymptotic rank transform. Compared with test procedures based on the original observations, the proposed rank procedures are free of moment conditions, converge to their limiting distribution faster, and have better power when the underlying distributions are heavy tailed or skewed. These advantages are demonstrated by simulations and an application to a real data set.

UR - http://www.scopus.com/inward/record.url?scp=70449432706&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70449432706&partnerID=8YFLogxK

U2 - 10.1080/10485250902971757

DO - 10.1080/10485250902971757

M3 - Article

AN - SCOPUS:70449432706

VL - 21

SP - 663

EP - 681

JO - Journal of Nonparametric Statistics

JF - Journal of Nonparametric Statistics

SN - 1048-5252

IS - 6

ER -