On the factorization criterion for quantum statistics
Ewa Czkwianianc (2005)
Mathematica Slovaca
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Ewa Czkwianianc (2005)
Mathematica Slovaca
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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...
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,...
Irène Gannaz, Olivier Wintenberger (2010)
ESAIM: Probability and Statistics
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Assume that () is a real valued time series admitting a common marginal density with respect to Lebesgue's measure. [Donoho (1996) 508–539] propose near-minimax estimators based on thresholding wavelets to estimate f on a compact set in an independent and identically distributed setting. The aim of the present work is to extend these results to general weak dependent contexts. Weak dependence assumptions are expressed as decreasing bounds of covariance terms and...
Chandrawansa, Kumari, Ruymgaart, Frits H., van Rooij, Arnoud C.M. (2000)
Journal of Applied Mathematics and Stochastic Analysis
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