A Semi-parametric Approach to Mode Estimation for Continuous Data

Abstract

In this talk we propose a semi-parametric approach for estimating the mode of an unknown density function. The approach is based on a weighted average of a parametric density estimate derived from Box-Cox transform and a nonparametric kernel density estimate. The proposed mode estimate is the maximizer of the mixture density estimates. The approach has two advantages. One is that it can efficiently reduce as much variability caused by the kernel density estimate as possible at small sample sizes. The other is that the mode estimate still converges to the true mode even if the parametric density estimate is unsuitable. The simulated examples herein demonstrate that the proposed mode estimate via the semi-parametric approach indeed performs excellently at small to large sample sizes. Finally, some theoretical results are given. Keywords：Box-Cox transform, kernel density, integrated square error ?