A theoretic study of a distance-based regression model

doi:10.1007/s11425-017-9295-7

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	A theoretic study of a distance-based regression model
	Li, Jialu 1; Zhang, Wei 2; Zhang, Sanguo 3,4; Li, Qizhai5
	2019-05-01
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	62 期号:5 页码:979-998
摘要	The distance-based regression model has many applications in analysis of multivariate response regression in various fields, such as ecology, genomics, genetics, human microbiomics, and neuroimaging. It yields a pseudo F test statistic that assesses the relation between the distance (dissimilarity) of the subjects and the predictors of interest. Despite its popularity in recent decades, the statistical properties of the pseudo F test statistic have not been revealed to our knowledge. This study derives the asymptotic properties of the pseudo F test statistic using spectral decomposition under the matrix normal assumption, when the utilized dissimilarity measure is the Euclidean or Mahalanobis distance. The pseudo F test statistic with the Euclidean distance has the same distribution as the quotient of two Chi-squared-type mixtures. The denominator and numerator of the quotient are approximated using a random variable of the form xi chi(2)(d) + eta, and the approximate error bound is given. The pseudo F test statistic with the Mahalanobis distance follows an F distribution. In simulation studies, the approximated distribution well matched the "exact" distribution obtained by the permutation procedure. The obtained distribution was further validated on H1N1 influenza data, aging human brain data, and embryonic imprint data.
关键词	distance-based regression Euclidean pseudo F test statistic Mahalanobis
DOI	10.1007/s11425-017-9295-7
语种	英语
资助项目	National Natural Science Foundation of China[11722113]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000464866600009
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/34478
专题	系统科学研究所
通讯作者	Li, Qizhai
作者单位	1.Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China 2.NICHHD, Biostat & Bioinformat Branch, Bethesda, MD 20817 USA 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 4.Chinese Acad Sci, Key Lab Big Data Min & Knowledge Management, Beijing 100190, Peoples R China 5.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, LSC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Li, Jialu,Zhang, Wei,Zhang, Sanguo,et al. A theoretic study of a distance-based regression model[J]. SCIENCE CHINA-MATHEMATICS,2019,62(5):979-998.
APA	Li, Jialu,Zhang, Wei,Zhang, Sanguo,&Li, Qizhai.(2019).A theoretic study of a distance-based regression model.SCIENCE CHINA-MATHEMATICS,62(5),979-998.
MLA	Li, Jialu,et al."A theoretic study of a distance-based regression model".SCIENCE CHINA-MATHEMATICS 62.5(2019):979-998.