R package hgam: High-dimensional Additive Modelling. We propose a new sparsity-smoothness penalty for high-dimensional generalized additive models. The combination of sparsity and smoothness is crucial for mathematical theory as well as performance for finite-sample data. We present a computationally efficient algorithm, with provable numerical convergence properties, for optimizing the penalized likelihood. Furthermore, we provide oracle results which yield asymptotic optimality of our estimator for high dimensional but sparse additive models. Finally, an adaptive version of our sparsity-smoothness penalized approach yields large additional performance gains.

References in zbMATH (referenced in 73 articles , 1 standard article )

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  1. Feng, Yang; Wu, Yichao; Stefanski, Leonard A.: Nonparametric independence screening via favored smoothing bandwidth (2018)
  2. He, Yong; Zhang, Xinsheng; Zhang, Liwen: Variable selection for high dimensional Gaussian copula regression model: an adaptive hypothesis testing procedure (2018)
  3. Huang, Tao; Li, Jialiang: Semiparametric model average prediction in panel data analysis (2018)
  4. Lv, Shaogao; Lin, Huazhen; Lian, Heng; Huang, Jian: Oracle inequalities for sparse additive quantile regression in reproducing kernel Hilbert space (2018)
  5. Suzuki, Taiji: Fast learning rate of non-sparse multiple kernel learning and optimal regularization strategies (2018)
  6. Huet, Sylvie; Taupin, Marie-Luce: Metamodel construction for sensitivity analysis (2017)
  7. Lv, Shaogao; He, Xin; Wang, Junhui: A unified penalized method for sparse additive quantile models: an RKHS approach (2017)
  8. Reese, Timothy; Mojirsheibani, Majid: On the (L_p) norms of kernel regression estimators for incomplete data with applications to classification (2017)
  9. Scornet, Erwan: Tuning parameters in random forests (2017)
  10. Amato, Umberto; Antoniadis, Anestis; De Feis, Italia: Additive model selection (2016)
  11. Biau, Gérard; Fischer, Aurélie; Guedj, Benjamin; Malley, James D.: COBRA: a combined regression strategy (2016)
  12. Christmann, Andreas; Zhou, Ding-Xuan: Learning rates for the risk of kernel-based quantile regression estimators in additive models (2016)
  13. Ginsbourger, David; Roustant, Olivier; Durrande, Nicolas: On degeneracy and invariances of random fields paths with applications in Gaussian process modelling (2016)
  14. Goia, Aldo (ed.); Vieu, Philippe (ed.): An introduction to recent advances in high/infinite dimensional statistics (2016)
  15. Kwemou, Marius: Non-asymptotic oracle inequalities for the Lasso and group Lasso in high dimensional logistic model (2016)
  16. Shah, Rajen D.: Modelling interactions in high-dimensional data with backtracking (2016)
  17. Xia, Xiaochao; Liu, Zhi; Yang, Hu: Regularized estimation for the least absolute relative error models with a diverging number of covariates (2016)
  18. Zhang, Yichi; Staicu, Ana-Maria; Maity, Arnab: Testing for additivity in non-parametric regression (2016)
  19. Fan, Yingying; James, Gareth M.; Radchenko, Peter: Functional additive regression (2015)
  20. Hu, Yuao; Zhao, Kaifeng; Lian, Heng: Bayesian quantile regression for partially linear additive models (2015)

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