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Sparse High-dimensional Varying Coefficient Model : Non-asymptotic Minimax Study

  • Olga Klopp

    ()

    (CREST and University Paris- Nanterre)

  • Marianna Pensky

    (University of Central Florida)

Registered author(s):

    The objective of the present paper is to develop a minimax theory for the varying coefficient model in a non-asymptotic setting. We consider a high- dimensional sparse varying coefficient model where only few of the covariates are present and only some of those covariates are time dependent. Our analysis allows the time dependent covariates to have different degrees of smoothness and to be spatially inhomogeneous. We develop the minimax lower bounds for the quadratic risk and construct an adaptive estimator which attains those lower bounds within a constant (if all time-dependent covariates are spatially homogeneous) or logarithmic factor of the number of observations.

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    Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2013-30.

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    Length: 24
    Date of creation: Dec 2013
    Date of revision:
    Handle: RePEc:crs:wpaper:2013-30
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    1. 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.
    2. Lijian Yang & Byeong U. Park & Lan Xue & Wolfgang Härdle, 2005. "Estimation and Testing for Varying Coefficients in Additive Models with Marginal Integration," SFB 649 Discussion Papers SFB649DP2005-047, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Jianhua Z. Huang & Haipeng Shen, 2004. "Functional Coefficient Regression Models for Non-linear Time Series: A Polynomial Spline Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(4), pages 515-534.
    4. Lukas Meier & Sara van de Geer & Peter Bühlmann, 2008. "The group lasso for logistic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 53-71.
    5. Arnak Dalalyan & Yuri Ingster & Alexandre B. Tsybakov, 2012. "Statistical Inference in Compound Functional Models," Working Papers 2012-20, Centre de Recherche en Economie et Statistique.
    6. Wang, Lan & Kai, Bo & Li, Runze, 2009. "Local Rank Inference for Varying Coefficient Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1631-1645.
    7. Şentürk, Damla & Müller, Hans-Georg, 2010. "Functional Varying Coefficient Models for Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1256-1264.
    8. Jianhua Z. Huang, 2002. "Varying-coefficient models and basis function approximations for the analysis of repeated measurements," Biometrika, Biometrika Trust, vol. 89(1), pages 111-128, March.
    9. Li, Gaorong & Xue, Liugen & Lian, Heng, 2011. "Semi-varying coefficient models with a diverging number of components," Journal of Multivariate Analysis, Elsevier, vol. 102(7), pages 1166-1174, August.
    10. Karim Lounici & Massimiliano Pontil & Alexandre B. Tsybakov & Sara Van De Geer, 2010. "Oracle Inequalities and Optimal Inference under Group Sparsity," Working Papers 2010-35, Centre de Recherche en Economie et Statistique.
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