In this note, we consider the performance of the classic method of moments for parameter estimation of symmetric variance-gamma (generalized Laplace) distributions. We do this through both theoretical analysis (multivariate delta method) and a comprehensive simulation study with comparison to maximum likelihood estimation, finding performance is often unsatisfactory. In addition, we modify the method of moments by taking absolute moments to improve efficiency; in particular, our simulation studies demonstrate that our modified estimators have significantly improved performance for parameter values typically encountered in financial modelling, and is also competitive with maximum likelihood estimation.

翻译：本文研究了对称方差伽马（广义拉普拉斯）分布参数估计中经典矩估计法的性能。通过理论分析（多元德尔塔方法）及与最大似然估计对比的全面模拟研究，发现经典矩估计法的性能往往不尽如人意。此外，我们采用绝对矩对矩估计法进行修正以提升效率；特别地，模拟研究表明，在金融建模中常见参数取值情形下，修正后的估计量性能显著提升，且与最大似然估计具有竞争力。