QUANTILE ESTIMATION WITH ADAPTIVE IMPORTANCE SAMPLING

被引：20

作者：

Egloff, Daniel ^{[1
]}

Leippold, Markus ^{[2
]}

机构：

[1] QuantCatalyst, CH-8000 Zurich, Switzerland

[2] Univ Zurich, Swiss Banking Inst, CH-8032 Zurich, Switzerland

来源：

ANNALS OF STATISTICS | 2010年 / 38卷 / 02期

基金：

瑞士国家科学基金会;

关键词：

Quantile estimation; law of iterated logarithm; adaptive importance sampling; stochastic approximation; Robbins-Monro; STOCHASTIC-APPROXIMATION; CONVERGENCE;

D O I：

10.1214/09-AOS745

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：1244 / 1278

页数：35

共 34 条

[1] Stability of stochastic approximation under verifiable conditions [J].