Penalized contrast estimator for adaptive density deconvolution

By Fabienne Comte, Yves Rozenholc, Marie-Luce Taupin. 2006

125 citations recorded by the source corpus.

The authors consider the problem of estimating the density g of independent and identically distributed variables XI, from a sample Z1,… Zn such that ZI = XI + σϵ for i = 1,…, n, and E is noise independent of X, with σϵ having a known distribution. They present a model selection procedure allowing one to construct an adaptive estimator of g and to find nonasymptotic risk bounds. The estimator achieves the minimax rate of convergence, in most cases where lower bounds are available. A simulation study gives an illustration of the good practical performance of the method.

Subfields: Artificial Intelligence, Computer Networks and Communications, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1f060ec95c7580fa537caf0ca5ae63ee807326ee

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In Artificial Intelligence

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Citations in the corpus

A ridge-parameter approach to deconvolution (2007, methodology): “For recent examples, see Delaigle and Gijbels [9, 10] in the setting of kernel techniques, and Comte, Rozenholc and Taupin [6, 7] for penalization methods.”
Adaptive functional linear regression (2011, methodology): “es for the constant κ, though convenient for deriving the theory, are far too large in practice. In our simulation study they are instead determined by means of preliminary simulations as proposed in [11], for example. The next assertion provides an upper risk-bound for the data-driven thresholded p”
Adaptive estimation of linear functionals in the convolution model and applications (2009, unknown): “For example, this happens if ψ is supersmooth when ε is ordinary smooth.”
Rates of convergence for nonparametric deconvolution (2006, unknown): “Un estimateur adaptatif peut ensuite être défini en utilisant une technique de sélection de modèles (voir [4] pour les détails).”
Generalized Non-Parametric Deconvolution with an Application to Earnings Dynamics (2010, methodology): “sample of size N , we first estimate κY and its derivatives by empirical analogs, replacing the mathematical expectations in (7), (8) and (9) by arithmetic means:”
Data‐driven density estimation in the presence of additive noise with unknown distribution (2011, methodology): “For νn,1, we use the following proposition, which was mainly proved in Comte et al. (2006).”