On an Auxiliary Function for Log-Density Estimation

TL;DR

This paper introduces explicit formulas for a special function used in nonparametric log-density estimation, facilitating computations in high-dimensional settings and supporting the R-package 'LogCondDEAD'.

Contribution

It provides explicit expressions and expansions for a key function in nonparametric log-density estimation, aiding implementation and analysis.

Findings

Derived explicit formulas for the special function.

Enhanced understanding of the function's properties and expansions.

Supported practical applications in R-package 'LogCondDEAD'.

Abstract

In this note we provide explicit expressions and expansions for a special function which appears in nonparametric estimation of log-densities. This function returns the integral of a log-linear function on a simplex of arbitrary dimension. In particular it is used in the R-package "LogCondDEAD" by Cule et al. (2007).