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.

摘要

在与预测相关的实际问题中，有时会发生经典回归估计的信息量不足以对响应变量做出良好预测的情况。当多模态、不对称或异方差噪声表征基础分布函数时，通常会发生这种情况。在这种情况下，条件模式估计可能构成预测的替代方法，因为条件密度更适合描述解释性数据向量与目标变量之间的关联。在本文中，我们推导出 psi 弱依赖条件下核条件密度和模式函数估计器的收敛率。建立了模式函数估计器的渐近分布，并通过仿真研究说明了所提出估计器的准确性。