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- W2040751215 abstract "Barron estimators are modified histograms depending on some reference probability density. They have been proved to have good consistency properties according to several information theoretical criteria. In this Note, Barron estimators are viewed as dynamical systems in a functional space with the reference density as initial state. Properties of stationary densities of these systems are investigated. It is then proved, under some assumptions, that the trajectories become almost surely stationary after a finite number of iterations. Les estimateurs de Barron sont des histogrammes modifiés construits à partir d'une densité de probabilité dite de référence. Ces estimateurs sont connus pour posséder de bonnes propriétés de convergence au sens des critères de la théorie de l'information. Dans cette Note, nous envisageons les estimateurs de Barron comme des systèmes dynamiques fonctionnels pour lesquels la densité de référence joue le rôle de la condition initiale. Nous étudions les propriétés des densités stationnaires de ces systèmes et nous démontrons, sous certaines hypothèses, que les trajectoires deviennent presque sûrement stationnaires après un nombre fini d'itérations." @default.
- W2040751215 created "2016-06-24" @default.
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- W2040751215 date "2001-03-01" @default.
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- W2040751215 title "Iterated Barron density estimators" @default.
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- W2040751215 doi "https://doi.org/10.1016/s0764-4442(01)01858-4" @default.
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