Displaying similar documents to “Controlling the Gibbs phenomenon in noisy deconvolution of irregular multivariable input signals.”

Minimax and bayes estimation in deconvolution problem

Mikhail Ermakov (2008)

ESAIM: Probability and Statistics

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We consider a deconvolution problem of estimating a signal blurred with a random noise. The noise is assumed to be a stationary Gaussian process multiplied by a weight function function where and is a small parameter. The underlying solution is assumed to be infinitely differentiable. For this model we find asymptotically minimax and Bayes estimators. In the case of solutions having finite number of derivatives similar results were obtained in [G.K. Golubev and R.Z. Khasminskii,...

Plug-in estimators for higher-order transition densities in autoregression

Anton Schick, Wolfgang Wefelmeyer (2009)

ESAIM: Probability and Statistics

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In this paper we obtain root- consistency and functional central limit theorems in weighted -spaces for plug-in estimators of the two-step transition density in the classical stationary linear autoregressive model of order one, assuming essentially only that the innovation density has bounded variation. We also show that plugging in a properly weighted residual-based kernel estimator for the unknown innovation density improves on plugging in an unweighted residual-based...

Asymptotic normality of the integrated square error of a density estimator in the convolution model.

Cristina Butucea (2004)

SORT

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In this paper we consider a kernel estimator of a density in a convolution model and give a central limit theorem for its integrated square error (ISE). The kernel estimator is rather classical in minimax theory when the underlying density is recovered from noisy observations. The kernel is fixed and depends heavily on the distribution of the noise, supposed entirely known. The bandwidth is not fixed, the results hold for any sequence of bandwidths decreasing to 0. In particular the...

Penalized estimators for non linear inverse problems

Jean-Michel Loubes, Carenne Ludeña (2010)

ESAIM: Probability and Statistics

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In this article we tackle the problem of inverse non linear ill-posed problems from a statistical point of view. We discuss the problem of estimating an indirectly observed function, without prior knowledge of its regularity, based on noisy observations. For this we consider two approaches: one based on the Tikhonov regularization procedure, and another one based on model selection methods for both ordered and non ordered subsets. In each case we prove consistency of the estimators...

An alternative analysis of variance.

Nicholas T. Longford (2008)

SORT

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The one-way analysis of variance is a staple of elementary statistics courses. The hypothesis test of homogeneity of the means encourages the use of the selected-model based estimators which are usually assessed without any regard for the uncertainty about the outcome of the test. We expose the weaknesses of such estimators when the uncertainty is taken into account, as it should be, and propose synthetic estimators as an alternative.