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• W3014721733 abstract "Deconvolution is a statistical inverse problem to estimate the distribution of a random variable based on its noisy observations. Despite the extensive studies on the topic, deconvolution with unknown noise distribution remains as a notoriously hard problem. We propose a matrix-based viewpoint for collective deconvolution that subsumes the setup with repeated measurements as a special case. As the main result, we describe a simple algorithm that partially utilizes matrix structure to solve deconvolution problem and provide non-asymptotic error analysis for the algorithm. We show that the proposed algorithm achieves the minimax optimal rate for deconvolution in a restricted sense. We also remark the connection between the collective deconvolution and the so-called statistical seriation as a byproduct or our matrix viewpoint. We conjecture that the link suggests that collective deconvolution, as well as deconvolution with repeated measurements, is intrinsically much easier than usual deconvolution of a single distribution." @default.
• W3014721733 created "2020-04-10" @default.
• W3014721733 creator A5029499294 @default.
• W3014721733 creator A5056798043 @default.
• W3014721733 date "2018-03-09" @default.
• W3014721733 modified "2023-09-27" @default.
• W3014721733 title "Deconvolution with Unknown Error Distribution Interpreted as Blind Isotonic Regression" @default.
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• W3014721733 hasPublicationYear "2018" @default.
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