Convergence of D\"umbgen's Algorithm for Estimation of Tail Inflation

Jasha Sommer-Simpson

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arXiv · 1906.04544

Convergence of D\"umbgen's Algorithm for Estimation of Tail Inflation

Jasha Sommer-Simpson

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Abstract

Given a density $f$ on the non-negative real line, D\"umbgen's algorithm is a routine for finding the (unique) log-convex, non-decreasing function $\hat\phi$ such that $\int\hat\phi(x)f(x)dx=1$ and such that the likelihood $\prod_{i=1}^{n}f(x_i)\hat\phi(x_i)$ of given data $x_1,\ldots,x_n$ under density $x\mapsto \hat\phi(x)f(x)$ is maximized. We summarize D\"umbgen's algorithm for finding this MLE $\hat\phi$, and we present a novel guarantee of the algorithm's termination and convergence.

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Jasha Sommer-Simpson. 2019-06-08. Convergence of D\"umbgen's Algorithm for Estimation of Tail Inflation. https://arxiv.org/abs/1906.04544

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