Optimal convergence rates for Good's nonparametric maximum likelihood density estimator

• 成果类型: Article
• 署名作者: Eggermont, PPB; LaRiccia, VN
• 署名单位: University of Delaware
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1999
• 页码: 1600-1615
• 关键词: penalized likelihood; selection

摘要

We study maximum penalized likelihood density estimation using the first roughness penalty functional of Good. We prove a simple pointwise comparison result with a kernel estimator based on the two-sided exponential kernel. This leads to L(1) convergence results similar to those for kernel estimators. We also prove Hellinger distance bounds for the roughness penalized estimator.