Estimating monotone densities by cellular binary trees

03/15/2022

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by   Luc Devroye, et al.

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We propose a novel, simple density estimation algorithm for bounded monotone densities with compact support under a cellular restriction. We show that its expected error (L_1 distance) converges at a rate of n^-1/3, that its expected runtime is sublinear and, in doing so, find a connection to the theory of Galton–Watson processes.