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Joint rank and variable selection for parsimonious estimation in a high-dimensional finite mixture regression model

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  • Devijver, Emilie

Abstract

We study a dimensionality reduction technique for finite mixtures of high-dimensional multivariate response regression models. Both the dimension of the response and the number of predictors are allowed to exceed the sample size. We consider predictor selection and rank reduction to obtain lower-dimensional approximations. A class of estimators with a fast rate of convergence is introduced. We apply this result to a specific procedure, introduced in Devijver (in press), where the relevant predictors are selected by the Group-Lasso.

Suggested Citation

  • Devijver, Emilie, 2017. "Joint rank and variable selection for parsimonious estimation in a high-dimensional finite mixture regression model," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 1-13.
    • Handle: RePEc:eee:jmvana:v:157:y:2017:i:c:p:1-13
    DOI: 10.1016/j.jmva.2017.02.006
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    References listed on IDEAS

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    1. Nicolas Städler & Peter Bühlmann & Sara Geer, 2010. "ℓ 1 -penalization for mixture regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 209-256, August.
    2. Khalili, Abbas & Chen, Jiahua, 2007. "Variable Selection in Finite Mixture of Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1025-1038, September.
    3. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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