In this paper, we propose two kernel distribution estimators based on a data transformation. We study the properties of these estimators and we compare them with two conventional estimators. It appears that with an appropriate choice of the parameters of the two proposed estimators, the convergence rate of two estimators will be faster than that of the two conventional estimators and the Mean Integrated Square Error will be smaller than the two conventional estimators. We corroborate these theoretical results through simulations as well as a real data set.

中文翻译：

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基于数据转换的两个新的非参数内核分布估计量

在本文中，我们提出了基于数据转换的两个内核分布估计量。我们研究了这些估计量的性质，并将它们与两个常规估计量进行了比较。看来，有两个建议估计的参数的适当选择，两个估计的收敛速度将快于这两个传统估计，平均综合方误差会比这两个传统估计较小。我们通过模拟和真实数据来证实这些理论结果。