A note on rank reduction in sparse multivariate regression

Kun Chen, Kung-Sik Chan
2015 Journal of Statistical Theory and Practice  
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
more » ... ic 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. We generalize the RSSVD approach to conduct rank reduction, variable selection, and model estimation simultaneously. Although the true rank r* is unknown, an upper bound of Chen and Chan
doi:10.1080/15598608.2015.1081573 pmid:26997938 pmcid:PMC4797956 fatcat:nspjrdbz3rg47bblolvpgmbuoq