TY - JOUR
T1 - Inference for mixed models of ANOVA type with high-dimensional data
AU - Chen, Fei
AU - Li, Zaixing
AU - Shi, Lei
AU - ZHU, Lixing
N1 - Funding Information:
A subset of the CASTNet data has been used only for illustrative purpose of our methodology. We thank the United States Environmental Protection Agency (EPA) for providing the data. The US EPA is not responsible for the content of this document or its implications. The research described here was supported by a grant from the Research Grants Council of Hong Kong , the grants from the National Natural Science Foundation of China (Grant Nos. 11126297 , 11261064 and 11001267 ) and the grant from Applied and Basic Research Plan of Yunnan Province (Grant No. 2011FZ151 ). We thank the associate editor and two anonymous referees for their careful reading of the original manuscript and for their comments, which helped to improve the article. Appendix A
PY - 2015/1/1
Y1 - 2015/1/1
N2 - Inference for variance components in linear mixed models of ANOVA type, including estimation and testing, has been investigated when the number of fixed effects is fixed. However, for high-dimensional data, this number is large and would be regarded as a divergent value as the sample size goes to infinity. In this paper, existing tests are extended to handle this problem with a sparse model structure. To avoid the impact from insignificant fixed effects, the proposed tests are post-selection-based with an orthogonality-based selection of SCAD type applied to selecting significant fixed effects into working model. The selection and estimation of fixed effects are under the assumption on the existence of second order moments for errors. Two types of tests for random effects are considered and some new insights are obtained. The proposed tests are distribution-free, though they request the existence of the fourth moments of random effects and errors. The proposed methods are illustrated by simulation studies and a real data analysis.
AB - Inference for variance components in linear mixed models of ANOVA type, including estimation and testing, has been investigated when the number of fixed effects is fixed. However, for high-dimensional data, this number is large and would be regarded as a divergent value as the sample size goes to infinity. In this paper, existing tests are extended to handle this problem with a sparse model structure. To avoid the impact from insignificant fixed effects, the proposed tests are post-selection-based with an orthogonality-based selection of SCAD type applied to selecting significant fixed effects into working model. The selection and estimation of fixed effects are under the assumption on the existence of second order moments for errors. Two types of tests for random effects are considered and some new insights are obtained. The proposed tests are distribution-free, though they request the existence of the fourth moments of random effects and errors. The proposed methods are illustrated by simulation studies and a real data analysis.
KW - 62H15
KW - Fixed effect selection
KW - Linear mixed model
KW - Shrinkage estimation
KW - Test for variance components
UR - http://www.scopus.com/inward/record.url?scp=84910072331&partnerID=8YFLogxK
U2 - 10.1016/j.jmva.2014.09.013
DO - 10.1016/j.jmva.2014.09.013
M3 - Journal article
AN - SCOPUS:84910072331
SN - 0047-259X
VL - 133
SP - 382
EP - 401
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
ER -