Costa, Manon, Gadat, Sébastien, Gonnord, Pauline and Risser, Laurent (2019) Cytometry inference through adaptive atomic deconvolution. Journal of Nonparametric Statistics, vol. 31 (n° 2). pp. 506-547.

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Identification Number : 10.1080/10485252.2019.1599376


In this paper, we consider a statistical estimation problem known as atomic deconvolution. Introduced in reliability, this model has a direct application when considering biological data produced by flow cytometers. From a statistical point of view, we aim at inferring the percentage of cells expressing the selected molecule and the probability distribution function associated with its fluorescence emission. We propose here an adaptive estimation procedure based on a previous deconvolution procedure introduced by Es, Gugushvili, and Spreij [(2008), ‘Deconvolution for an atomic distribution’, Electronic Journal of Statistics, 2, 265–297] and Gugushvili, Es, and Spreij [(2011), ‘Deconvolution for an atomic distribution: rates of convergence’, Journal of Nonparametric Statistics, 23, 1003–1029]. For both estimating the mixing parameter and the mixing density automatically, we use the Lepskii method based on the optimal choice of a bandwidth using a bias-variance decomposition. We then derive some convergence rates that are shown to be minimax optimal (up to some log terms) in Sobolev classes. Finally, we apply our algorithm on the simulated and real biological data.

Item Type: Article
Language: English
Date: April 2019
Refereed: Yes
Place of Publication: Philadelphia
Uncontrolled Keywords: Mixture models, atomic deconvolution, adaptive kernel estimators, inverse problems
Divisions: TSE-R (Toulouse)
Site: UT1
Date Deposited: 01 Oct 2019 13:49
Last Modified: 27 Oct 2021 13:37
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