Convergence of Dümbgen's Algorithm for Estimation of Tail Inflation

Abstract

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 $\hat{\varphi }$ such that $\int \hat{\varphi }(x)f(x)dx=1$ and such that the likelihood ${\prod }_{i=1}^{n}f(x_i)\hat{\varphi }(x_i)$ of given data $x_1,\dots ,x_n$ under density $x\mapsto \hat{\varphi }(x)f(x)$ is maximized. We summarize Dümbgen's algorithm for finding this MLE $\hat{\varphi }$, and we present a novel guarantee of the algorithm's termination and convergence.

UChicago MS thesis

Cited by in corpus (1)

• Active set algorithms for estimating shape-constrained density ratios