基于余弦核函数在Solve-the-Equation方法下的核密度估计

Solve-the-Equation Kernel Density Estimation Method Based on Cosine Kernel Function

核概率密度函数估计是对未知的概率密度函数进行估计的一种方法,其中关键是对核函数的选取以及窗口宽度的确定.利用Solve-the-Equation方法对窗宽中存在的二阶导数进行推导,设计迭代算法得出在Solve-the-Equation方法下的最优窗口宽度.在核方法确定的情况下,利用余弦核函数对未知的概率密度函数进行估计,并对改进核函数进行估计,找到最优的余弦核函数,通过验证得出改进后的核函数其估计精度和平滑度都有所提高.

Kernel probability density function estimation is a method to estimate unknown probability density function, and the key of kernel probability density function estimation method is the selection of kernel function and the determination of bandwidth. In this paper, the Solve-the-Equation method is used to derive the second deriva- tive of the bandwidth, and the iterative algorithm is designed to calaulate the optimal bandwidth. Under the premise of the determinate kernel method, cosine kernel is used to estimate unknown probability density function and make an improvement. Results show that the new kernel function improves the precision and gliding property of kernel density estimation.