Statistics Group



Nonparametric Inference

Bull, Chen, Gach, Kueh, Lounici, Nickl, Pitts, Samworth

Nonparametric inference aims to identify very general processes from the data they generate. CSI is making cutting-edge contributions to understanding the theoretical properties and applied significance of nonparametric techniques. A major challenge is to develop automatic procedures that do not require a priori knowledge or arbitrary choices. In adaptive estimation the data themselves are used to select the right amount of smoothing or tuning, e.g., for thresholding empirical wavelet coefficients or other variable bandwidth methods. Another approach assumes only nonparametric shape constraints, such as monotonicity, convexity or log-concavity of an unknown function, and aims to identify and compute fully automatic estimators. A further strand of research concentrates on nonparametric estimation for risk and queueing models.

RS3 RS2 RS1
Fully automatic nonparametric density estimation.



  • Cule, M.L., Samworth, R.J. and Stewart, M.I. (2010).
    Maximum likelihood estimation of a multi-dimensional log-concave density.
    Journal of the Royal Statistical Society, Series B. (with discussion), 72, 545-607.
  • Hansen, M.B. and Pitts, S.M. (2010)
    Decompounding random sums.
    Annals of the Institute of Statistical Mathematics, 62 855-872.
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  • Dumbgen, L., Samworth, R. J. and Schuhmacher, D. (2011).
    Approximation by log-concave distributions with applications to regression.
    Annals of Statistics, to appear.
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  • Lounici, K. and Nickl, R. (2011)
    Global Uniform Risk Bounds for Wavelet Deconvolution Estimators.
    Annals of Statistics, 39, 201-231.
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  • Gine, E. and Nickl R. (2010).
    Confidence Bands in Density Estimation.
    Annals of Statistics, 38, 1122-1170.
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  • Samworth, R. J. and Wand, M. P. (2010).
    Asymptotics and optimal bandwidth selection for highest density region estimation.
    Annals of Statistics, 38, 1767-1792.
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  • M. Hoffmann, R. Nickl (2011)
    On adaptive inference and confidence band
    Annals of Statistics, to appear