Kernel conditional density and mode estimation for psi-weakly dependent observations

Abstract

In practical problems connected with forecasting, it sometimes happens that the classical regression estimation is not informative enough to make good predictions of a response variable. This occurs typically when multi-modality, asymmetry, or heteroscedastic noise characterizes the underlying distribution function. In this situation, conditional mode estimation may constitute an alternative method to prediction, because conditional density is more adequate to describe the association between an explanatory data vector and a target variable. In this paper we derive rates of convergence for kernel conditional density and mode functions estimators under psi-weak dependence condition. The asymptotic distribution of the mode function estimator is established and the accuracy of the proposed estimators is illustrated via a simulation study.