Structured Nonparametric Curve Estimation

  • Enno MammenEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 208)


In this note, we discuss structured nonparametric models. Under a structured nonparametric model, we understand a non- or semiparametric model with several nonparametric components where one of the nonparametric components lies in the focus of statistical interest but where all other nonparametric components are nuisance parameters. In structured nonparametrics, the focus of the statistical analysis is inference on this component whereas the goodness of fit of the whole model is only of secondary interest. This creates new challenging problems in the theory of nonparametrics. We will outline this in this note by discussing two classes of models from structured nonparametrics and by highlighting the theoretical questions arising in these classes of models.


Structured nonparametrics Kernel smoothing Nonparametric additive models Chain ladder mode 


  1. 1.
    Gregory, K., Mammen, E., Wahl, M: Optimal estimation of sparse high-dimensional additive models, Preprint (2016)Google Scholar
  2. 2.
    Horowitz, J., Klemelä, J., Mammen, E.: Optimal estimation in additive regression models. Bernoulli 12, 271–298 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Horowitz, J., Mammen, E.: Rate-optimal estimation for a general class of nonparametric regression models with unknown link functions. Ann. Statist. 35, 2589–2619 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Koltchinskii, V., Yuan, M.: Sparse recovery in large ensembles of kernel machines. In: Servedio, R.A., Zhang, T. (eds.) Colt, pp. 229–238. Omnipress, Madison (2008)Google Scholar
  5. 5.
    Lee, Y.K., Mammen, E., Nielsen, J.P., Park, B.U.: Asymptotics for In-Sample Density Forecasting. Ann. Statist. 43, 620–645 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Lee, Y.K., Mammen, E., Nielsen, J.P., Park, B.U.: Operational time and in-sample density forecasting, Ann. Statist. 45, 1312–1341 (2017)Google Scholar
  7. 7.
    Lu, J., Kolar,M., Liu, H.: Post-regularization confidence bands for high dimensional nonparametric models with local sparsity, Technical Report (2015) arXiv:1503.02978
  8. 8.
    Mammen, E., Martínez Miranda, M.D., Nielsen, J.P.: In-sample forecasting applied to reserving and mesothelioma. Insur.: Math. Econ. 61, 76–86 (2015)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Meier, L., van de Geer, S., Bühlmann, P.: High-dimensional additive modeling. Ann. Statist. 37, 3779–3821 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Raskutti, G., Wainwright, M.J., Yu, B.: Minimax-optimal rates for sparse additive models over kernel classes via convex programming. J. Mach. Learn. Res. 13, 389–427 (2012)MathSciNetzbMATHGoogle Scholar
  11. 11.
    van de Geer, S., Muro, A.: Penalized least squares estimation in the additive model with different smoothness for the components. J. Statist. Planning and Inf. 162, 43–61 (2015)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Heidelberg UniversityHeidelbergGermany

Personalised recommendations