Goodness-of-fit testing strategies from indirect observations

被引：2

作者：

Loubes, J. M. ^{[1
]}

Marteau, C. ^{[1
]}

机构：

[1] Inst Math Toulouse, F-31077 Toulouse 4, France

来源：

JOURNAL OF NONPARAMETRIC STATISTICS | 2014年 / 26卷 / 01期

关键词：

SIGNAL-DETECTION; CONTAMINATED SAMPLE; INVERSE PROBLEMS; MINIMAX RATES; DECONVOLUTION; CONVERGENCE; SELECTION;

D O I：

10.1080/10485252.2013.827680

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider in this paper a goodness-of-fit testing problem in a density framework. In particular, we deal with an error-in-variables model where each new incoming observation is gathered with a random independent error. It is well known that in such a situation, we are faced with an inverse (deconvolution) problem. Nevertheless, following recent results in the Gaussian white noise model, we prove that using procedures containing a deconvolution step is not always necessary. © 2013 © 2013 American Statistical Association and Taylor & Francis.

引用

页码：85 / 99

页数：15

共 20 条

[1] Baraud Y, 2003, ANN STAT, V31, P225
[2] Baraud Y, 2002, BERNOULLI, V8, P577
[3] Convergence rates of general regularization methods for statistical inverse problems and applications
Bissantz, N.
Hohage, T.
Munk, A.
Ruymgaart, F.
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2007, 45 (06) : 2610 - 2636
[4] Testing for lack of fit in inverse regression-with applications to biophotonic imaging
Bissantz, Nicolai
Claeskens, Gerda
Holzmann, Hajo
Munk, Axel
[J]. JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 2009, 71 : 25 - 48
[5] Sharp optimality in density deconvolution with dominating bias. I
Butucea, C.
Tsybakov, A. B.
[J]. THEORY OF PROBABILITY AND ITS APPLICATIONS, 2008, 52 (01) : 24 - 39
[6] Goodness-of-fit testing and quadratic functional estimation from indirect observations
Butucea, Cristina
[J]. ANNALS OF STATISTICS, 2007, 35 (05) : 1907 - 1930
[7] Adaptive goodness-of-fit testing from indirect observations
Butucea, Cristina
Matias, Catherine
Pouet, Christophe
[J]. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2009, 45 (02): : 352 - 372
[8] Nonparametric statistical inverse problems
Cavalier, L.
[J]. INVERSE PROBLEMS, 2008, 24 (03)
[9] Bootstrap bandwidth selection in kernel density estimation from a contaminated sample
Delaigle, A
Gijbels, I
[J]. ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 2004, 56 (01) : 19 - 47
[10] Engl H. W., 1996, REGULARIZATION INVER

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