Convergence of Dümbgen's Algorithm for Estimation of Tail Inflation

06/08/2019

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by   Jasha Sommer-Simpson, et al.

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Given a density f on the non-negative real line, Dümbgen's algorithm is a routine for finding the (unique) log-convex, non-decreasing function ϕ̂ such that ∫ϕ̂(x)f(x)dx=1 and such that the likelihood ∏_i=1^nf(x_i)ϕ̂(x_i) of given data x_1,...,x_n under density xϕ̂(x)f(x) is maximized. We summarize Dümbgen's algorithm for finding this MLE ϕ̂, and we present a novel guarantee of the algorithm's termination and convergence.