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Matching a Distribution by Matching Quantiles Estimation

Author

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  • Nikolaos Sgouropoulos
  • Qiwei Yao
  • Claudia Yastremiz

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.

Suggested Citation

  • Nikolaos Sgouropoulos & Qiwei Yao & Claudia Yastremiz, 2015. "Matching a Distribution by Matching Quantiles Estimation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 742-759, June.
    • Handle: RePEc:taf:jnlasa:v:110:y:2015:i:510:p:742-759
    DOI: 10.1080/01621459.2014.929522
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    Cited by:

    1. Jacobi, Arie & Tzur, Joseph, 2021. "Wealth Distribution across Countries: Quality of Weibull, Dagum and Burr XII in Estimating Wealth over Time," Finance Research Letters, Elsevier, vol. 43(C).
    2. Qin, Shanshan & Wu, Yuehua, 2020. "General matching quantiles M-estimation," Computational Statistics & Data Analysis, Elsevier, vol. 147(C).

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