Title :

Quadratic functional estimation in inverse problems

Author(s) :

Butucea, Cristina [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Meziani, Katia [Auteur]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]

Journal title :

Statistical Methodology

Pages :

31-41

Publisher :

Elsevier

Publication date :

2010-05

ISSN :

1572-3127

English keyword(s) :

second order risk
Gaussian sequence model
inverse problem
minimax upper bounds
parametric rate
Pinsker estimator
projection estimator
quadratic functional
second order risk.

HAL domain(s) :

Mathématiques [math]/Statistiques [math.ST]
Statistiques [stat]/Théorie [stat.TH]

English abstract : [en]

In this paper, we consider a Gaussian sequence of independent observations having a polynomially increasing variance. This model describes a large panel of inverse problems, such as the deconvolution of blurred images or ...
Show more >In this paper, we consider a Gaussian sequence of independent observations having a polynomially increasing variance. This model describes a large panel of inverse problems, such as the deconvolution of blurred images or the recovering of the fractional derivative of a signal. We estimate the sum of squares of the means of our observations. This quadratic functional has practical meanings, e.g. the energy of a signal, and it is often used for goodness-of-fit testing. We compute Pinsker estimators when the underlying signal has both a finite and infinite amount of smoothness. When the signal is sufficiently smoother than the difficulty of the inverse problem, we attain the parametric rate and the efficiency constant associated with it. Moreover, we give upper bounds of the second order term in the risk. Otherwise, when the parametric rate cannot be attained, we compute non parametric upper bounds of the risk.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL