On bandwidth choice for density estimation with dependent data

• 成果类型: Article
• 署名作者: Hall, P; Lahiri, SN; Truong, YK
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill; Iowa State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1995
• 页码: 2241-2263
• 关键词: nonparametric density; REGRESSION ESTIMATION; Cross-validation; markov sequences; kernel; CONVERGENCE; Consistency; selection; ORDER

摘要

We address the empirical bandwidth choice problem in cases where the range of dependence may be virtually arbitrarily long. Assuming that the observed data derive from an unknown function of a Gaussian process, it is argued that, unlike more traditional contexts of statistical inference, in density estimation there is no clear role for the classical distinction between short- and long-range dependence. Indeed, the ''boundaries'' that separate different modes of behaviour for optimal bandwidths and mean squared errors are determined more by kernel order than by traditional notions of strength of dependence, for example, by whether or not the sum of the covariances converges. We provide surprising evidence that, even for some strongly dependent data sequences, the asymptotically optimal bandwidth for independent data is a good choice. A plug-in empirical bandwidth selector based on this observation is suggested. We determine the properties of this choice for a wide range of different strengths of dependence. Properties of cross-validation are also addressed.