Functional Median Polish

Ying Sun; Marc G. Genton

doi:10.1007/s13253-012-0096-8

Functional Median Polish

Ying Sun, Marc G. Genton

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

This article proposes functional median polish, an extension of univariate median polish, for one-way and two-way functional analysis of variance (ANOVA). The functional median polish estimates the functional grand effect and functional main factor effects based on functional medians in an additive functional ANOVA model assuming no interaction among factors. A functional rank test is used to assess whether the functional main factor effects are significant. The robustness of the functional median polish is demonstrated by comparing its performance with the traditional functional ANOVA fitted by means under different outlier models in simulation studies. The functional median polish is illustrated on various applications in climate science, including one-way and two-way ANOVA when functional data are either curves or images. Specifically, Canadian temperature data, U. S. precipitation observations and outputs of global and regional climate models are considered, which can facilitate the research on the close link between local climate and the occurrence or severity of some diseases and other threats to human health.

Original language	English (US)
Pages (from-to)	354-376
Number of pages	23
Journal	Journal of Agricultural, Biological, and Environmental Statistics
Volume	17
Issue number	3
DOIs	https://doi.org/10.1007/s13253-012-0096-8
State	Published - Sep 2012
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This research was partially supported by NSF grants DMS-1007504, DMS-1100492, and Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). The authors thank Bo Li, Guest Editor, and two referees for valuable comments, as well as Caspar M. Ammann for providing the GCM data analyzed in Section 4.3.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

Keywords

Analysis of variance
Climate models
Functional data
Health
Image data
Median polish
Robustness
Spatio-temporal data

ASJC Scopus subject areas

General Environmental Science
Applied Mathematics
Agricultural and Biological Sciences (miscellaneous)
General Agricultural and Biological Sciences
Statistics and Probability
Statistics, Probability and Uncertainty

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1007/s13253-012-0096-8

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title = "Functional Median Polish",

abstract = "This article proposes functional median polish, an extension of univariate median polish, for one-way and two-way functional analysis of variance (ANOVA). The functional median polish estimates the functional grand effect and functional main factor effects based on functional medians in an additive functional ANOVA model assuming no interaction among factors. A functional rank test is used to assess whether the functional main factor effects are significant. The robustness of the functional median polish is demonstrated by comparing its performance with the traditional functional ANOVA fitted by means under different outlier models in simulation studies. The functional median polish is illustrated on various applications in climate science, including one-way and two-way ANOVA when functional data are either curves or images. Specifically, Canadian temperature data, U. S. precipitation observations and outputs of global and regional climate models are considered, which can facilitate the research on the close link between local climate and the occurrence or severity of some diseases and other threats to human health.",

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author = "Ying Sun and Genton, {Marc G.}",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: This research was partially supported by NSF grants DMS-1007504, DMS-1100492, and Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). The authors thank Bo Li, Guest Editor, and two referees for valuable comments, as well as Caspar M. Ammann for providing the GCM data analyzed in Section 4.3. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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PY - 2012/9

Y1 - 2012/9

N2 - This article proposes functional median polish, an extension of univariate median polish, for one-way and two-way functional analysis of variance (ANOVA). The functional median polish estimates the functional grand effect and functional main factor effects based on functional medians in an additive functional ANOVA model assuming no interaction among factors. A functional rank test is used to assess whether the functional main factor effects are significant. The robustness of the functional median polish is demonstrated by comparing its performance with the traditional functional ANOVA fitted by means under different outlier models in simulation studies. The functional median polish is illustrated on various applications in climate science, including one-way and two-way ANOVA when functional data are either curves or images. Specifically, Canadian temperature data, U. S. precipitation observations and outputs of global and regional climate models are considered, which can facilitate the research on the close link between local climate and the occurrence or severity of some diseases and other threats to human health.

AB - This article proposes functional median polish, an extension of univariate median polish, for one-way and two-way functional analysis of variance (ANOVA). The functional median polish estimates the functional grand effect and functional main factor effects based on functional medians in an additive functional ANOVA model assuming no interaction among factors. A functional rank test is used to assess whether the functional main factor effects are significant. The robustness of the functional median polish is demonstrated by comparing its performance with the traditional functional ANOVA fitted by means under different outlier models in simulation studies. The functional median polish is illustrated on various applications in climate science, including one-way and two-way ANOVA when functional data are either curves or images. Specifically, Canadian temperature data, U. S. precipitation observations and outputs of global and regional climate models are considered, which can facilitate the research on the close link between local climate and the occurrence or severity of some diseases and other threats to human health.

KW - Analysis of variance

KW - Climate models

KW - Functional data

KW - Health

KW - Image data

KW - Median polish

KW - Robustness

KW - Spatio-temporal data

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Functional Median Polish

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

UN SDGs

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