A theoretic study of a distance-based regression model
文献类型：期刊论文
| 作者 | Li, Jialu3; Zhang, Wei4; Zhang, Sanguo1,5; Li, Qizhai2
|
| 刊名 | SCIENCE CHINA-MATHEMATICS
 |
| 出版日期 | 2019-05-01 |
| 卷号 | 62期号:5页码:979-998 |
| 关键词 | distance-based regression Euclidean pseudo F test statistic Mahalanobis |
| ISSN号 | 1674-7283 |
| DOI | 10.1007/s11425-017-9295-7 |
| 英文摘要 | 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. |
| 资助项目 | National Natural Science Foundation of China[11722113] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000464866600009 |
| 出版者 | SCIENCE PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/34477]  |
| 专题 | 系统科学研究所 |
| 通讯作者 | Li, Qizhai |
| 作者单位 | 1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, LSC, Beijing 100190, Peoples R China 3.Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China 4.NICHHD, Biostat & Bioinformat Branch, Bethesda, MD 20817 USA 5.Chinese Acad Sci, Key Lab Big Data Min & Knowledge Management, 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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