An Automatic Bandwidth Selector for Kernel Density Estimation
针对交叉验证选择带宽时变异性大的问题，提出通过修改样本特征函数并推广交叉验证来选取截止频率，从而得到收敛速度更快的带宽估计量，模拟和实际数据均显示优势。
To select a proper bandwidth is a critical step in kernel density estimation. It is well known that the bandwidth selected by cross-validation has a large variability. This difficulty limits the applicability of cross-validation. To reduce the variability, we suggested modifying the sample characteristic function beyond some cut-off frequency in estimating the bias term of the mean integrated squared error. It is proposed to select the cut-off frequency by a generalization of cross-validation. For smooth density functions, the asymptotic distribution of the bandwidth estimator based on the estimated cut-off frequency is obtained. The proposed bandwidth estimator has a relative convergence rate n−½, which is much faster than the rate n−½ for the bandwidth estimate selected by cross-validation. A modification which reduces the chance of selecting a large cut-off frequency is also suggested. In simulation studies, the advantages of the proposed procedures are clearly demonstrated. The procedures are also applied to some data sets.