Multiple-merger coalescents, also known as $\Lambda$-coalescents, have been used to describe the genealogy of populations that have a skewed offspring distribution or that undergo strong selection. Inferring the characteristic measure $\Lambda$, which describes the rates of the multiple-merger events, is key to understand these processes. So far, most inference methods only work for some particular families of $\Lambda$-coalescents that are described by only one parameter, but not for more general models. This article is devoted to the construction of a non-parametric estimator of the density of $\Lambda$ that is based on the observation at a single time of the so-called Site Frequency Spectrum (SFS), which describes the allelic frequencies in a present population sample. First, we produce estimates of the multiple-merger rates by solving a linear system, whose coefficients are obtained by appropriately subsampling the SFS. Then, we use a technique that aggregates the information extracted from the previous step through a kernel type of re-construction to give a non-parametric estimation of the measure $\Lambda$. We give a consistency result of this estimator under mild conditions on the behavior of $\Lambda$ around 0. We also show some numerical examples of how our method performs.

多重合并成膜助剂，也称为$\Lambda$- 聚结体，已被用来描述具有倾斜后代分布或经历强烈选择的种群的谱系。推断特征测量$\Lambda$描述了多重合并事件的发生率，是理解这些过程的关键。到目前为止，大多数推理方法仅适用于某些特定的家族$\Lambda$-仅由一个参数描述的聚结剂，但不适用于更一般的模型。本文致力于构建一个非参数密度估计器$\Lambda$这是基于对所谓的位点频谱 (SFS) 的单个时间的观察，它描述了当前群体样本中的等位基因频率。首先，我们通过求解线性系统来产生多重合并率的估计，其系数是通过对 SFS 进行适当的二次采样获得的。然后，我们使用一种技术，通过内核类型的重构来聚合从上一步中提取的信息，以给出度量的非参数估计$\Lambda$。我们给出了该估计器在温和条件下的行为的一致性结果$\Lambda$大约 0。我们还展示了一些我们的方法如何执行的数值示例。