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.

We study here the kernel type, non-parametric estimation of the conditional hazard function, based on a sample of functional dependent data. The almost complete convergence of the conditional hazard estimate is easily derived using the properties referred by Ferraty et al for the conditional distribution and conditional density estimates. The asymptotic bias and variances of the three estimates (conditional density, distribution and hazard) are calculated and compared with the results obtained in p-dimensional non-parametric kernel estimation. The asymptotic normality is established for the three mentioned estimates. Finally, an application to an earthquake data set is made.

Nonparametric Kernel Distribution Function Estimation with kerdiest: An R Package for Bandwidth Choice and Applications