A note on density mode estimation

Four nonparametric estimates of the mode of a density function are investigated. Two mode estimates are defined from a global (resp. from a local) kernel density estimate, while the other two are defined from a global (resp. from a local) kernel estimate of the first derivative of the density function. We show that each of these mode estimates attains the same rate of convergence as the usual sample model (Eddy, 1980). Then, Monte-Carlo simulations illustrate on finite samples the utility of the method based on the local estimate of the first derivative.