Estimating moments in ANOVA-type mixed models

Zaixing Li; Fei Chen; Lixing ZHU

doi:10.1007/s00184-017-0623-2

Estimating moments in ANOVA-type mixed models

Zaixing Li, Fei Chen, Lixing ZHU^*

^*Corresponding author for this work

Department of Mathematics

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

Abstract

In the paper, a simple projection-based method is systematically developed to estimate the qth (q≥ 2) order moments of random effects and errors in the ANOVA type mixed model (ANOVAMM), where the response may not be divided into independent sub-vectors. All the estimates are weakly consistent and the second-order moment estimates are strongly consistent. Besides, the derived estimates are different from those in mixed models with cluster design. Simulation studies are conducted to examine the finite sample performance of the estimates and two real data examples are analyzed for illustration.

Original language	English
Pages (from-to)	697-715
Number of pages	19
Journal	Metrika
Volume	80
Issue number	6-8
DOIs	https://doi.org/10.1007/s00184-017-0623-2
Publication status	Published - 1 Nov 2017

Scopus Subject Areas

Statistics and Probability
Statistics, Probability and Uncertainty

User-Defined Keywords

Non-normal distributions
qth order moments
Random effects

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10.1007/s00184-017-0623-2

Cite this

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title = "Estimating moments in ANOVA-type mixed models",

abstract = "In the paper, a simple projection-based method is systematically developed to estimate the qth (q≥ 2) order moments of random effects and errors in the ANOVA type mixed model (ANOVAMM), where the response may not be divided into independent sub-vectors. All the estimates are weakly consistent and the second-order moment estimates are strongly consistent. Besides, the derived estimates are different from those in mixed models with cluster design. Simulation studies are conducted to examine the finite sample performance of the estimates and two real data examples are analyzed for illustration.",

keywords = "Non-normal distributions, qth order moments, Random effects",

author = "Zaixing Li and Fei Chen and Lixing ZHU",

note = "Funding Information: Acknowledgements The authors thank the editor, the associate editor and a referee for their constructive suggestions that substantially improved an earlier manuscript. The research was supported by the National Natural Science Foundation of China (11671398, 11001267, 11261064), the State Key Lab of Coal Resources and Safe Mining (No. SKLCRSM16KFB03), the Fundamental Research Funds for the Central Universities in China (2009QS02), the Beijing Youth Talent Program (No. YETP0945), and a grant from Research Grants Council of Hong Kong, Hong Kong. Funding Information: This research was supported by a grant from the University Grants Council of Hong Kong, Hong Kong, China, and a Grant (NSFC11671042) from the Natural Science Foundation of China.",

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doi = "10.1007/s00184-017-0623-2",

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AU - Chen, Fei

AU - ZHU, Lixing

N1 - Funding Information: Acknowledgements The authors thank the editor, the associate editor and a referee for their constructive suggestions that substantially improved an earlier manuscript. The research was supported by the National Natural Science Foundation of China (11671398, 11001267, 11261064), the State Key Lab of Coal Resources and Safe Mining (No. SKLCRSM16KFB03), the Fundamental Research Funds for the Central Universities in China (2009QS02), the Beijing Youth Talent Program (No. YETP0945), and a grant from Research Grants Council of Hong Kong, Hong Kong. Funding Information: This research was supported by a grant from the University Grants Council of Hong Kong, Hong Kong, China, and a Grant (NSFC11671042) from the Natural Science Foundation of China.

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N2 - In the paper, a simple projection-based method is systematically developed to estimate the qth (q≥ 2) order moments of random effects and errors in the ANOVA type mixed model (ANOVAMM), where the response may not be divided into independent sub-vectors. All the estimates are weakly consistent and the second-order moment estimates are strongly consistent. Besides, the derived estimates are different from those in mixed models with cluster design. Simulation studies are conducted to examine the finite sample performance of the estimates and two real data examples are analyzed for illustration.

AB - In the paper, a simple projection-based method is systematically developed to estimate the qth (q≥ 2) order moments of random effects and errors in the ANOVA type mixed model (ANOVAMM), where the response may not be divided into independent sub-vectors. All the estimates are weakly consistent and the second-order moment estimates are strongly consistent. Besides, the derived estimates are different from those in mixed models with cluster design. Simulation studies are conducted to examine the finite sample performance of the estimates and two real data examples are analyzed for illustration.

KW - Non-normal distributions

KW - qth order moments

KW - Random effects

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JF - Metrika

IS - 6-8

ER -

Estimating moments in ANOVA-type mixed models

Abstract

Scopus Subject Areas

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