In this paper, we study the asymptotic behavior of the kernel bivariate distribution function estimator for negatively superadditive dependent. The exponential convergence rates for the kernel estimator are investigated. Under certain regularity conditions, the optimal bandwidth rate is determined with respect to mean squared error criteria. A simulation study is used to justify the behavior of the kernel and histogram estimators. As an application, a real data set in hydrology is considered and the kernel bivariate distribution function estimator of the data is investigated.

中文翻译：

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NSD假设下核双变量分布函数估计量的指数收敛速度及其在水文数据中的应用

在本文中，我们研究了负超加性相关项的核双变量分布函数估计量的渐近行为。研究了核估计量的指数收敛速度。在某些规则性条件下，相对于均方误差标准确定最佳带宽速率。仿真研究用于证明核和直方图估计器的行为合理。作为一种应用，考虑了水文学中的真实数据集，并研究了数据的核双变量分布函数估计器。