A nonparametric conditional mode estimate

This paper proposes a new nonparametric estimate of the conditional mode. This mode estimate is obtained from kernel smoothing of the first derivative of the conditional density function with location adaptive bandwidth. We give the rates of convergence of this estimate under general dependence conditions on the sample that make our results valid for nonparametric prediction of time series. As a by-products, we also get rate of convergence of the usual mode of a density function under dependence, and we give some extensions to local bandwidth of recent results on kernel estimation under mixing conditions.