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A theoretic study of a distance-based regression model
Li, Jialu1; Zhang, Wei2; Zhang, Sanguo3,4; Li, Qizhai5
2019-05-01
Source PublicationSCIENCE CHINA-MATHEMATICS
ISSN1674-7283
Volume62Issue:5Pages:979-998
AbstractThe 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.
Keyworddistance-based regression Euclidean pseudo F test statistic Mahalanobis
DOI10.1007/s11425-017-9295-7
Language英语
Funding ProjectNational Natural Science Foundation of China[11722113]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000464866600009
PublisherSCIENCE PRESS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/34478
Collection系统科学研究所
Corresponding AuthorLi, Qizhai
Affiliation1.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
Recommended Citation
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.
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