On Estimation of the Mode

Abstract

Let $Y_1, \cdots, Y_n$ be an ordered sample from a density with mode $\theta$. We propose to estimate $\theta$ by suitable points in the interval formed by the first and the last of those $s$ consecutive $Y_i$'s which are closest together. Choices of $s$ which yield consistency of these estimates, the speed of convergence and asymptotic distributions are discussed in this paper.