Nonparametric goodness-of fit testing in quantum homodyne tomography with noisy data

Details Nonparametric goodness-of fit testing in quantum homodyne tomography with noisy data Nonparametric goodness-of fit testing in quantum homodyne tomography with noisy data

2008-08-23

arxiv.org/abs/0808.3194v2

Electronic Journal of Statistics 2008, Vol. 2, 1195-1223

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/08-EJS286 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by t

Scientific paper

10.1214/08-EJS286

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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