A NOTE ON THE USEFULNESS OF SUPERKERNELS IN DENSITY-ESTIMATION

• 成果类型: Article
• 署名作者: DEVROYE, L
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348901
• 发表日期: 1992
• 页码: 2037-2056
• 关键词: square error properties; kernel; distance

摘要

We consider the Akaike-Parzen-Rosenblatt density estimate f(nh) based upon any superkernel L (i.e., an absolutely integrable function with integral L = 1, whose characteristic function is 1 on [-1, 1]), and compare it with a kernel estimate g(nh) based upon an arbitrary kernel K. We show that for a given subclass of analytic densities, [GRAPHICS] where h > 0 is the smoothing factor. Thus, asymptotically, the class of superkernels is as good as any other class of kernels when certain analytic densities are estimated. We also obtain exact asymptotic expressions for the expected L1 error of the kernel estimate when superkernels are used.