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Last edited on
Oct 17, 2024 by JJ.
Jan JOHANNES Mar 01,2018 Talks
Talk (.pdf):
13th German Open Conference on Probability and Statistics in Freiburg, Germany

Presented by:
Jan JOHANNES

Title:
Data-driven estimation by aggregation based on a penalised contrast criterion

Abstract:
We consider the non-parametric estimation of a function f based on an orthogonal series approach. Given a family of orthogonal series estimators of f indexed by a dimension parameter m belonging to a pre-specified collection M the selection of a dimension parameter as a minimiser of a penalised contrast criterion leads in many cases to an optimal estimator of f in an oracle or minimax sense. In this work we propose a fully data-driven aggregation of the series estimators using random weights, which shares the optimality properties of the estimator with data-driven selected dimension parameter. The construction of the random weights is inspired by the recent work of Johannes et al. [2015] where a fully data-driven Bayes estimator in an indirect sequence space model with hierarchical prior is constructed. Notably, the construction of the random weights allows to caracterise the estimator with data-driven selected dimension parameter as a limit case of the data-driven aggregation strategy. As illustration we consider non-parametric regression with random design and non-parametric density estimation and we discuss its potential extension to deconvolution models as well as non-parametric inverse regression.

References:
Comte, F., Johannes, J. and Loizeau, X. (2018). Data-driven aggregated circular deconvolution with unknown error distribution. Discussion paper in preparation, Heidelberg University
Johannes, J. (2018). Adaptive aggregated Gaussian inverse regression with partially known operator. Discussion paper in preparation, Heidelberg University
Johannes, J. and Schwarz, M. (2013). Adaptive Gaussian inverse regression with partially unknown operator. Communications in Statistics - Theory and Methods, 42(7):1343-1362.
Johannes, J. and Schwarz, (2013). Adaptive circular deconvolution by model selection under unknown error distribution. Bernoulli, 19(5A):1576-1611.
Johannes, J., Simoni, A. and Schenk, R. (2015). Adaptive Bayesian estimation in indirect Gaussian sequence space models. Discussion paper, arXiv:1502.00184.