Sliced inverse regression method for multivariate compositional data modeling

被引：0
作者：
Huiwen Wang
Zhichao Wang
Shanshan Wang
机构：
[1] Beihang University,School of Economics and Management
[2] Beijing Advanced Innovation Center for Big Data and Brain Computing,undefined
[3] Beijing Key Laboratory of Emergence Support Simulation Technologies for City Operations,undefined
来源：
Statistical Papers | 2021年 / 62卷
关键词：
Effective dimension reduction; Multivariate compositional data; Sliced inverse regression; Total covariance matrix; Simplicial multiple normal distribution;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Compositional data modeling is of great practical importance, as exemplified by applications in economic and geochemical data analysis. In this study, we investigate the sliced inverse regression (SIR) procedure for multivariate compositional data with a scalar response. We can achieve dimension reduction for the original multivariate compositional data quickly and then conduct a regression on the dimensional-reduced compositions. It is documented that the proposed method is successful in detecting effective dimension reduction directions, which generalizes the theoretical framework of SIR to multivariate compositional data. Comprehensive simulation studies are conducted to evaluate the performance of the proposed SIR procedure and the simulation results show its feasibility and effectiveness. A real data application is finally used to illustrate the success of the proposed SIR-based method.
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页码：361 / 393
页数：32
相关论文
共 83 条
[1]  
Aitchison J(1982)The statistical analysis of compositional data J R Stat Soc 44 139-177
[2]  
Aitchison J(1983)Principal component analysis of compositional data Biometrika 70 57-65
[3]  
Aitchison J(1984)Log contrast models for experiments with mixtures Biometrika 71 323-330
[4]  
Bacon-Shone J(2003)Characterization of distributional forms for compositional data and associated distributional tests Math Geol 35 667-680
[5]  
Aitchison J(2014)Spatio-temporal regression on compositional covariates: modeling vegetation in a gypsum outcrop Environ Ecol Stat 22 1-19
[6]  
Mateu-Figueras G(2016)Non-parametric regression on compositional covariates using Bayesian P-splines Stat Methods Appl 25 75-88
[7]  
Ng KW(2017)Student sliced inverse regression Comput Stat Data Anal 113 441-456
[8]  
Bruno F(2005)Groups of parts and their balances in compositional data analysis Math Geol 37 795-828
[9]  
Greco F(2003)Isometric logratio transformations for compositional data analysis Math Geol 35 279-300
[10]  
Ventrucci M(2009)Principal component analysis for compositional data with outliers Environmetrics 20 621-632
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