Mobius-like mappings and their use in kernel density estimation

• 成果类型: Article
• 署名作者: Clements, A; Hurn, S; Lindsay, K
• 署名单位: Queensland University of Technology (QUT); University of Glasgow
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214503000000945
• 发表日期: 2003
• 页码: 993-1000
• 关键词: Bandwidth selection

摘要

It is well known that the manipulation of sample data by means of a parametric function can improve the performance of kernel density estimation. This article proposes a two-parameter Mobius-like function to map sample data drawn from a semi-infinite space into [-1, 1). A standard kernel method is then used to estimate the density. The proposed method is shown to yield effective estimates of density and is computationally more efficient than other well-known transformation methods. The efficacy of the technique is demonstrated in a practical setting by application to two datasets.