ASYMPTOTICS FOR THE TRANSFORMATION KERNEL DENSITY ESTIMATOR

• 成果类型: Article
• 署名作者: HOSSJER, O; RUPPERT, D
• 署名单位: Cornell University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176324705
• 发表日期: 1995
• 页码: 1198-1222
• 关键词: Bias

摘要

An asymptotic expansion is provided for the transformation kernel density estimator introduced by Ruppert and Cline. Let h(k) be the bandwidth used in the kth iteration, k = 1, 2,..., t. If all bandwidths are of the same order, the leading bias term of the lth derivative of the tth iterate of the density estimator has the form (b) over bar(t)((l))(x)Pi(k=1)(t) h(k)(2), where the bias factor (b) over bar(t)(x) depends on the second moment of the kernel K, as well as on all derivatives of the density f up to order 2t. In particular, the leading bias term is of the same order as when using an ordinary kernel density estimator with a kernel of order 2t. The leading stochastic term involves a kernel of order 2t that depends on K, h(l) and h(k)/f(x), k = 2,..., t.