Making a non-parametric density estimator more attractive, and more accurate, by data perturbation

• 成果类型: Article
• 署名作者: Doosti, Hassan; Hall, Peter
• 署名单位: Mashhad University of Medical Sciences; University of Melbourne
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12120
• 发表日期: 2016
• 页码: 445-462
• 关键词: square error properties; kernel; regression; superkernels; constraints; SUBJECT

摘要

Motivated by both the shortcomings of high order density estimators, and the increasingly large data sets in many areas of modern science, we introduce new high order, non-parametric density estimators that are guaranteed to be positive and do not have highly oscillatory tails. Our approach is based on data perturbation, e.g. by tilting or data sharpening. It leads to new estimators that are more accurate than conventional kernel techniques that use positive kernels, but which nevertheless enjoy the positivity property, and are far less wiggly' than high order kernel estimators. We investigate performance by theoretical analysis and in a numerical study.