This paper studies kernel density estimation by stagewise minimization algorithm with a simple dictionary on U-divergence. We randomly split an i.i.d. sample into the two disjoint sets, one to be used for constructing the kernels in the dictionary and the other for evaluating the estimator, and implement the algorithm. The resulting estimator brings us data-adaptive weighting parameters and bandwidth matrices, and realizes a sparse representation of kernel density estimation. We present the non-asymptotic error bounds of our estimator and confirm its performance by simulations compared with the direct plug-in bandwidth matrices and the reduced set density estimator.

翻译：本文通过一个简单的U- diverence字典,通过分阶段最小化算法来研究内核密度估计。 我们随机将一个i. d. 样本分解到两个不连接的组,一个用于在字典中建造内核,另一个用于评价估测器,并实施算法。 由此产生的测算器给我们带来了数据适应性加权参数和带宽矩阵,并实现了内核密度估计的稀疏表现。 我们展示了我们的估测器的非不方便误差界限,并通过与直接插载带宽矩阵和降低的定置密度估测仪相比的模拟来确认其性能。