Optimal Bandwidth Selection in Multivariate Kernel Density Estimation

• Main Author: 鄧宇凱
• Other Authors: 吳鐵肩
• Format: Others
• Language: zh-TW
• Published: 1997
• Online Access: http://ndltd.ncl.edu.tw/handle/51658515085157485470

碩士 === 國立東華大學 === 應用數學研究所 === 85 === Base on random sample of size n from an unknown d-dimensional density f, the problem of adaptively selecting the bandwidth in multivariate kernel density estimation of f is investigated. A stabilized bandiwdth selector, which extends the selector of Chiu (1992) from d=l to general d, is proposed in this thesis. It is well known that the bandwidth selected by the least-squares cross-validation has large variation. To reduce the variation, it was suggested to modify the sample characteristic function beyond some cut-off frequency in estimating the bias term of the mean integrated squared error. In simulation studies, the excellent performances of the proposed procedure are clear demonstrated. In particular, our stabilized bandwidth selection procedure is superior to the multivariate bootstrap procedure of Taylor (1989) , the least-squares cross-validation procedure, and the biased cross-validation of Sain, Baggerly, and Scott (1994).