Maximum Likelihood Estimation of a Unimodal Density, II

Abstract

This paper is a sequel to the earlier paper, "Maximum Likelihood Estimation of a Unimodal Density Function." The MLE of a unimodal density with unknown mode is shown to agree, for sufficiently large $n$ and on certain regions, with the MLE of a unimodal density with known mode. The asymptotic distributions of the MLE's then agree. Also a geometrical interpretation of the MLE of a unimodal density with unknown mode is given.