Sufficient Dimension Reduction for Multiple Compositional Predictors

Abstract

Motivated by research problems arising in the analysis of economic and geochemical data, we consider sufficient dimension reduction in regression with multiple compositional predictors. We develop a second-moment-based method that respects the unique features of compositional data. The proposed method is model-free and can fully recover the central dimension-reduction subspace, which then allows us to derive a sufficient reduction of the compositional predictors. In addition, we suggest a Bayesian-type information criterion to determine the structural dimension of the central subspace. Extensive simulation studies and an application to a disposable income of Chinese urban residents data set demonstrate the effectiveness and efficiency of the method.

Keywords

Compositional data / Sufficient dimension reduction / Moment-based inverse regression / Sliced average variance estimation

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Funding

natural science foundation of shanghai(19ZR1437000)

shanghai rising-star program(20QA1407500)

national natural science foundation of china(11971018)

National Natural Science Foundation of China(11971017)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature