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.
J. H. Venter. "On Estimation of the Mode." Ann. Math. Statist. 38 (5) 1446 - 1455, October, 1967. https://doi.org/10.1214/aoms/1177698699