title: Matching a Distribution by Matching Quantiles Estimation.
abstract: 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.
authors.forename: Nikolaos
authors.initials: N
authors.lastname: Sgouropoulos
authors.forename: Qiwei
authors.initials: Q
authors.lastname: Yao
authors.forename: Claudia
authors.initials: C
authors.lastname: Yastremiz
keywords: Goodness-of-match; LASSO; Ordinary least-squares estimation; Portfolio tracking; Representative portfolio; Sample quantile