Matching a Distribution by Matching Quantiles Estimation

• 成果类型: Article
• 署名作者: Sgouropoulos, Nikolaos; Yao, Qiwei; Yastremiz, Claudia
• 署名单位: University of London; London School Economics & Political Science; Peking University; Bank of England
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2014.929522
• 发表日期: 2015
• 页码: 742-759
• 关键词: tracking; tests

摘要

Motivated by the problem of selecting representative portfolios for backtesting counterparty credit risks, we propose a matching quantiles estimation (MQE) method for matching a target distribution by that of a linear combination of a set of random variables. An iterative procedure based on the ordinary least-squares estimation (OLS) is proposed to compute MQE. MQE can be easily modified by adding a LASSO penalty term if a sparse representation is desired, or by restricting the matching within certain range of quantiles to match a part of the target distribution. The convergence of the algorithm and the asymptotic properties of the estimation, both with or without LASSO, are established. A measure and an associated statistical test are proposed to assess the goodness-of-match. The finite sample properties are illustrated by simulation. An application in selecting a counterparty representative portfolio with a real dataset is reported. The proposed MQE also finds applications in portfolio tracking, which demonstrates the usefulness of combining MQE with LASSO.