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A note on rank reduction in sparse multivariate regression
Journal article   Peer reviewed

A note on rank reduction in sparse multivariate regression

Kun Chen and Kung-Sik Chan
Journal of Statistical Theory and Practice, Vol.10(1), pp.100-120
01/02/2016
DOI: 10.1080/15598608.2015.1081573
PMCID: PMC4797956
PMID: 26997938
url
https://www.ncbi.nlm.nih.gov/pmc/articles/4797956View
Open Access

Abstract

A reduced-rank regression with sparse singular value decomposition (RSSVD) approach was proposed by Chen et al. for conducting variable selection in a reduced-rank model. To jointly model the multivariate response, the method efficiently constructs a prespecified number of latent variables as some sparse linear combinations of the predictors. Here, we generalize the method to also perform rank reduction, and enable its usage in reduced-rank vector autoregressive (VAR) modeling to perform automatic rank determination and order selection. We show that in the context of stationary time-series data, the generalized approach correctly identifies both the model rank and the sparse dependence structure between the multivariate response and the predictors, with probability one asymptotically. We demonstrate the efficacy of the proposed method by simulations and analyzing a macro-economical multivariate time series using a reduced-rank VAR model.
 Primary 62J02 rank selection sparsity Reduced-rank singular value decomposition secondary 62M10 vector autoregressive model

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