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

Author

Listed:
  • Olga Klopp

    () (CREST and University Paris- Nanterre)

  • Marianna Pensky

    (University of Central Florida)

Abstract

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.

Suggested Citation

  • Olga Klopp & Marianna Pensky, 2013. "Sparse High-dimensional Varying Coefficient Model : Non-asymptotic Minimax Study," Working Papers 2013-30, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2013-30
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    References listed on IDEAS

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    3. 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.
    4. 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.
    5. Arnak Dalalyan & Yuri Ingster & Alexandre B. Tsybakov, 2012. "Statistical Inference in Compound Functional Models," Working Papers 2012-20, Center for Research in Economics and Statistics.
    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. Yang, Lijian & Park, Byeong U. & Xue, Lan & Hardle, Wolfgang, 2006. "Estimation and Testing for Varying Coefficients in Additive Models With Marginal Integration," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1212-1227, September.
    8. 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.
    9. Karim Lounici & Massimiliano Pontil & Alexandre B. Tsybakov & Sara Van De Geer, 2010. "Oracle Inequalities and Optimal Inference under Group Sparsity," Working Papers 2010-35, Center for Research in Economics and Statistics.
    10. 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.
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