A LAW OF THE LOGARITHM FOR KERNEL QUANTILE DENSITY ESTIMATORS

• 成果类型: Article
• 署名作者: XIANG, XJ
• 署名单位: University of Chicago
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176988741
• 发表日期: 1994
• 页码: 1078-1091
• 关键词: product-limit estimator

摘要

In this article we derive a law of the logarithm for the maximal deviation between two kernel-type quantile density estimators and the true underlying quantile density function in the randomly right-censored case. Extensions to higher derivatives are included. The results are applied to get optimal bandwidths with respect to almost sure uniform convergence.