Estimation of integrated squared density derivatives from a contaminated sample

• 成果类型: Article
• 署名作者: Delaigle, A; Gijbels, I
• 署名单位: Universite Catholique Louvain
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/1467-9868.00366
• 发表日期: 2002
• 页码: 869-886
• 关键词: optimal rates; deconvolution; CONVERGENCE

摘要

We propose a kernel estimator of integrated squared density derivatives, from a sample that has been contaminated by random noise. We derive asymptotic expressions for the bias and the variance of the estimator and show that the squared bias term dominates the variance term. This coincides with results that are available for non-contaminated observations. We then discuss the selection of the bandwidth parameter when estimating integrated squared density derivatives based on contaminated data. We propose a data-driven bandwidth selection procedure of the plug-in type and investigate its finite sample performance via a simulation study.