QUANTILE ESTIMATION WITH ADAPTIVE IMPORTANCE SAMPLING

• 成果类型: Article
• 署名作者: Egloff, Daniel; Leippold, Markus
• 署名单位: University of Zurich
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/09-AOS745
• 发表日期: 2010
• 页码: 1244-1278
• 关键词: stochastic-approximation; CONVERGENCE

摘要

We introduce new quantile estimators with adaptive importance sampling. The adaptive estimators are based on weighted samples that are neither independent nor identically distributed. Using a new law of iterated logarithm for martingales, we prove the convergence of the adaptive quantile estimators for general distributions with nonunique quantiles thereby extending the work of Feldman and Tucker [Ann. Math. Statist. 37 (1996) 451-457]. We illustrate the algorithm with an example from credit portfolio risk analysis.