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2008 Nonparametric goodness-of fit testing in quantum homodyne tomography with noisy data
Katia Meziani
Electron. J. Statist. 2: 1195-1223 (2008). DOI: 10.1214/08-EJS286

Abstract

In the framework of quantum optics, we study the problem of goodness-of-fit testing in a severely ill-posed inverse problem. A novel testing procedure is introduced and its rates of convergence are investigated under various smoothness assumptions. The procedure is derived from a projection-type estimator, where the projection is done in $\mathbb{L}_{2}$ distance on some suitably chosen pattern functions. The proposed methodology is illustrated with simulated data sets.

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Katia Meziani. "Nonparametric goodness-of fit testing in quantum homodyne tomography with noisy data." Electron. J. Statist. 2 1195 - 1223, 2008. https://doi.org/10.1214/08-EJS286

Information

Published: 2008
First available in Project Euclid: 16 December 2008

zbMATH: 1320.62101
MathSciNet: MR2461899
Digital Object Identifier: 10.1214/08-EJS286

Subjects:
Primary: 62G05 , 62G10 , 62G20
Secondary: 81V80

Keywords: density matrix , Goodness-of fit test , Minimax rates , Nonparametric test , Pattern Functions estimation , quantum homodyne tomography , Wigner function

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society

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