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Schluttenhofer S, Johannes J. Adaptive Minimax Testing for Circular Convolution. MATHEMATICAL METHODS OF STATISTICS 2021. [DOI: 10.3103/s1066530720020039] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Autin F, Clausel M, Freyermuth JM, Marteau C. Maxiset Point of View for Signal Detection in Inverse Problems. MATHEMATICAL METHODS OF STATISTICS 2019. [DOI: 10.3103/s1066530719030037] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Kroll M. Rate optimal estimation of quadratic functionals in inverse problems with partially unknown operator and application to testing problems. ESAIM-PROBAB STAT 2019. [DOI: 10.1051/ps/2018027] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Abstract
We consider the estimation of quadratic functionals in a Gaussian sequence model where the eigenvalues are supposed to be unknown and accessible through noisy observations only. Imposing smoothness assumptions both on the signal and the sequence of eigenvalues, we develop a minimax theory for this problem. We propose a truncated series estimator and show that it attains the optimal rate of convergence if the truncation parameter is chosen appropriately. Consequences for testing problems in inverse problems are equally discussed: in particular, the minimax rates of testing for signal detection and goodness-of-fit testing are derived.
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Koul HL, Song W, Zhu X. Goodness-of-fit testing of error distribution in linear measurement error models. Ann Stat 2018. [DOI: 10.1214/17-aos1627] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Jia W, Song W. Goodness-of-fit tests in linear EV regression with replications. METRIKA 2018. [DOI: 10.1007/s00184-018-0648-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Marteau C, Sapatinas T. Minimax signal detection under weak noise assumptions. MATHEMATICAL METHODS OF STATISTICS 2017. [DOI: 10.3103/s1066530717040032] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Loustau S, Marteau C. Minimax fast rates for discriminant analysis with errors in variables. BERNOULLI 2015. [DOI: 10.3150/13-bej564] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Ingster Y, Laurent B, Marteau C. Signal detection for inverse problems in a multidimensional framework. MATHEMATICAL METHODS OF STATISTICS 2015. [DOI: 10.3103/s1066530714040036] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Marteau C, Sapatinas T. A unified treatment for non-asymptotic and asymptotic approaches to minimax signal detection. STATISTICS SURVEYS 2015. [DOI: 10.1214/15-ss112] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Marteau C, Mathé P. General regularization schemes for signal detection in inverse problems. MATHEMATICAL METHODS OF STATISTICS 2014. [DOI: 10.3103/s1066530714030028] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Gendre X. Model selection and estimation of a component in additive regression. ESAIM-PROBAB STAT 2014. [DOI: 10.1051/ps/2012028] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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Loubes J, Marteau C. Goodness-of-fit testing strategies from indirect observations. J Nonparametr Stat 2013. [DOI: 10.1080/10485252.2013.827680] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Schmidt-Hieber J, Munk A, Dümbgen L. Multiscale methods for shape constraints in deconvolution: Confidence statements for qualitative features. Ann Stat 2013. [DOI: 10.1214/13-aos1089] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Comminges L, Dalalyan AS. Minimax testing of a composite null hypothesis defined via a quadratic functional in the model of regression. Electron J Stat 2013. [DOI: 10.1214/13-ejs766] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Laurent B, Loubes JM, Marteau C. Non asymptotic minimax rates of testing in signal detection with heterogeneous variances. Electron J Stat 2012. [DOI: 10.1214/12-ejs667] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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