This study focuses on statistical inference for the class of quasi-infinitely divisible (QID) distributions, which was recently introduced by Lindner, Pan and Sato (2018). The paper presents a Fourier approach, based on the analogue of the L{é}vy-Khintchine theorem with a signed spectral measure. We prove that for some subclasses of QID distributions, the considered estimates have polynomial rates of convergence. This is a remarkable fact when compared to the logarithmic convergence rates of similar methods for infinitely divisible distributions, which cannot be improved in general. We demonstrate the numerical performance of the algorithm using simulated examples.

翻译：本研究聚焦于由Lindner、Pan和Sato（2018）近期提出的准无穷可分（QID）分布类的统计推断问题。本文提出一种基于带符号谱测度的Lévy-Khintchine定理模拟的傅里叶方法。我们证明：对于QID分布的某些子类，所考虑的估计量具有多项式收敛速率。相较于无穷可分分布同类方法通常无法改进的对数收敛速率，这一发现具有重要意义。通过模拟实例，我们展示了该算法的数值性能。