Robust inference in linear mixed model with skew normal-symmetric error

doi:10.1007/s11464-017-0660-1

Front. Math. China

2017, Vol. 12

Issue (6) : 1483-1500 https://doi.org/10.1007/s11464-017-0660-1

RESEARCH ARTICLE

Robust inference in linear mixed model with skew normal-symmetric error

Mixia WU¹(

), Ye TIAN¹, Aiyi LIU²

¹. College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
². Biostatistics and Bioinformatics Branch, Eunice Kennedy Shriver National Institute of Child Health and Human Development, Bethesda, MD 20892, USA

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Abstract

Linear mixed effects models with general skew normal-symmetric (SNS) error are considered and several properties of the SNS distributions are obtained. Under the SNS settings, ANOVA-type estimates of variance components in the model are unbiased, the ANOVA-type F-tests are exact F-tests in SNS setting, and the exact confidence intervals for fixed effects are constructed. Also the power of ANOVA-type F-tests for components are free of the skewing function if the random effects normally distributed. For illustration of the main results, simulation studies on the robustness of the models are given by comparisons of multivariate skew-normal, multivariate skew normal-Laplace, multivariate skew normal-uniform, multivariate skew normal-symmetric, and multivariate normal distributed errors. A real example is provided for the illustration of the proposed method.

Keywords Skew normal-symmetric (SNS) ANOVA-type F-test mixed effect

Corresponding Author(s): Mixia WU

Issue Date: 27 November 2017

Cite this article:

Mixia WU,Ye TIAN,Aiyi LIU. Robust inference in linear mixed model with skew normal-symmetric error[J]. Front. Math. China, 2017, 12(6): 1483-1500.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-017-0660-1
https://academic.hep.com.cn/fmc/EN/Y2017/V12/I6/1483

1	Arellano-ValleR B, GentonM G. Fundamental skew distributions. J Multivariate Anal, 2005, 96: 93–116 https://doi.org/10.1016/j.jmva.2004.10.002
2	AzzaliniA. The skew-normal distribution and related multivariate families (with discussion). Scand J Stat, 2005, 32: 159–188 https://doi.org/10.1111/j.1467-9469.2005.00426.x
3	AzzaliniA, Dalla ValleA. The multivariate skew-normal distribution. Biometrika, 1996, 83: 715–726 https://doi.org/10.1093/biomet/83.4.715
4	GentonM G. Discussion of “The Skew-normal”. Scand J Stat, 2005, 32: 189–198 https://doi.org/10.1111/j.1467-9469.2005.00427.x
5	GuptaA K, ChangF C. Multivariate skew-symmetric distributions. Statist Probab Lett, 2003, 16: 643–646 https://doi.org/10.1016/S0893-9659(03)00060-0
6	HuangW J, ChenY H. Quadratic forms of multivariate skew normal-symmetric distributions. Statist Probab Lett, 2006, 76: 871–879 https://doi.org/10.1016/j.spl.2005.10.018
7	KhuriA I, MathewT, SinhaB K. Statistical Tests for Mixed Linear Models. New York: John Wiley & Sons, 1998 https://doi.org/10.1002/9781118164860
8	LachosV H, DeyD K, CanchoV G. Robust linear mixed models with skew-normal independent distributions from a Bayesian perspective. J Statist Plann Inference, 2009, 139: 4098–4110 https://doi.org/10.1016/j.jspi.2009.05.040
9	LachosV H, GhoshP, Arellano-ValleR B. Likelihood based inference for skew-normal independent linear mixed models. Statist Sinica, 2010, 20: 303–322
10	LairdN M, WareJ H. Random effects models for longitudinal data. Biometrics, 1982, 38: 963–974 https://doi.org/10.2307/2529876
11	MaY, GentonM G. Flexible class of skew-symmetric distributions. Scand J Stat, 2004, 31: 459–468 https://doi.org/10.1111/j.1467-9469.2004.03_007.x
12	NadarajahS, KotzS. Skewed distributions generated by the normal kernel.Statist Probab Lett, 2003, 65: 269–277 https://doi.org/10.1016/j.spl.2003.07.013
13	SearleS R, CasellaG, McCullochC E. Variance Components. New York: Wiley, 1992 https://doi.org/10.1002/9780470316856
14	WangS G, ChowS C. Advanced Linear Models: Theory and Applications. New York: Marcel Dekker, Inc, 1994
15	WuM X. Introduction to Linear Mixed Models. Beijing: Science Press, 2013 (in Chinese)
16	WuM X, WangS G. Simultaneous optimal estimates of fixed effects and variance components in the mixed model. Sci China, Ser A, 2004, 47: 787–799 https://doi.org/10.1007/BF03036995
17	WuM X, ZhaoJ, WangT H, ZhaoY. The ANOVA-type inference in linear mixed model with skew-normal error. J Syst Sci Complex, 2017, 30: 710–720 https://doi.org/10.1007/s11424-017-5253-2
18	YeR D, WangT H. Inferences in linear mixed model with skew-normal random effects. Acta Math Sin (Engl Ser), 2015, 31: 576–594 https://doi.org/10.1007/s10114-015-3326-5
19	YeR D, WangT H, GuptaA K. Tests in variance components models under skewnormal settings. Metrika, 2015, 78: 885–904 https://doi.org/10.1007/s00184-015-0532-1

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