Heteroscedastic one-way ANOVA and lack-of-fit tests

M. G. Akritas, N. Papadatos

Research output: Contribution to journalArticle

54 Citations (Scopus)

Abstract

Recent articles have considered the asymptotic behavior of the one-way analysis of variance (ANOVA) F statistic when the number of levels or groups is large. In these articles, the results were obtained under the assumption of homoscedasticity and for the case when the sample or group sizes n i remain fixed as the number of groups, a, tends to infinity. In this article, we study both weighted and unweighted test statistics in the heteroscedastic case. The unweighted statistic is new and can be used even with small group sizes. We demonstrate that an asymptotic approximation to the distribution of the weighted statistic is possible only if the group sizes tend to infinity suitably fast in relation to a. Our investigation of local alternatives reveals a similarity between lack-of-fit tests for constant regression in the present case of replicated observations and the case of no replications, which uses smoothing techniques. The asymptotic theory uses a novel application of the projection principle to obtain the asymptotic distribution of quadratic forms.

Original languageEnglish (US)
Pages (from-to)368-382
Number of pages15
JournalJournal of the American Statistical Association
Volume99
Issue number466
DOIs
StatePublished - Jun 1 2004

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Lack-of-fit Test
Analysis of variance
Statistic
Infinity
Homoscedasticity
Tend
F-statistics
Local Alternatives
Smoothing Techniques
Asymptotic Approximation
Asymptotic Theory
Quadratic form
Asymptotic distribution
Replication
Test Statistic
Regression
Asymptotic Behavior
Group size
Statistics
Projection

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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Heteroscedastic one-way ANOVA and lack-of-fit tests. / Akritas, M. G.; Papadatos, N.

In: Journal of the American Statistical Association, Vol. 99, No. 466, 01.06.2004, p. 368-382.

Research output: Contribution to journalArticle

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