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.

H3B-8800, an orally available small-molecule splicing modulator, induces lethality in spliceosome-mutant cancers

“…For all sequence analyses, background introns were sampled from a random subset of all genes with at least one intron expressed in the untreated cellular context ( n = 6,405 and n = 5,500 for K562 and NALM-6, respectively) that have an expression distribution that is not significantly different from those genes that contained intron retention events in the treated context, measured by Kruskal H test ( P = 0.12 and P = 0.55 for K562 and NALM-6, respectively). Genes with matching expression levels were identified using Matching Quantiles Estimation (MQE) in seaborn 39 . Ideally, background transcripts would also be matched on the basis of transcript turnover rate, however to our knowledge, a comprehensive database in the presented cellular contexts is not currently available.…”

Estimating the reference interval from a fixed effects meta‐analysis

“…Furthermore, for studies reported those summary statistics in addition to the mean and SD, the quantile-matching estimation (QME) may be used to better estimate the parameters of the within-study distribution. 36,37 While the methods presented in this article only use aggregated study-level data, future studies may consider estimating the reference interval by combing studies with individual participant data and studies with aggregated study-level data. Future work could also investigate the effect of subject characteristics, such as age, on the normal reference range by incorporating covariates in the meta-regression model.…”

Large deviations for method-of-quantiles estimators of one-dimensional parameters

“…Moreover numerical values for λ max θ 0 = 0 0.39 (and 0.61 by symmetry) θ 0 = 1/2 0.84 θ 0 = −1/2 1 − 0.84 = 0.16 (by symmetry) Logistic distribution (namely G in (12)). By (15) we have…”

“…We also recall (Dominicy and Veredas 2013) where the authors consider an indirect inference method based on the simulation of theoretical quantiles, or a function of them, when they are not available in a closed form. In (Sgouropoulos, Yao and Yastremiz 2015), an iterative procedure based on ordinary least-squares estimation is proposed to compute MQ estimators; such estimators can be easily modified by adding a LASSO penalty term if a sparse representation is desired, or by restricting the matching within a given range of quantiles to match a part of the target distribution. Quantiles and empirical quantiles represent a key tool also in quantitative risk management, where they are studied under the name of Value-at-Risk (see for instance (McNeil, Frey and Embrechts 2015)).…”