Cytometry inference through adaptive atomic deconvolution

Abstract

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.

Keywords

Replaces

Manon Costa, Sébastien Gadat, Pauline Gonnord, and Laurent Risser, “Cytometry inference through adaptive atomic deconvolution”, TSE Working Paper, n. 18-905, March 2018.

Reference

Manon Costa, Sébastien Gadat, Pauline Gonnord, and Laurent Risser, “Cytometry inference through adaptive atomic deconvolution”, Journal of Nonparametric Statistics, vol. 31, n. 2, April 2019, pp. 506–547.