Adaptive estimation of the mode of a multivariate density

Estimation of the location of the mode of a multivariate density function is studied. We use the maximizer of a kernel estimator as an estimator for the location of the mode and we discuss the choice of the smoothing parameter of the kernel estimator to be maximized. This smoothing parameter is chosen in an adaptive way, that is, without assuming knowledge of the smoothness of the density function. It is proved that the proposed method has the optimal adaptive rate of convergence.