This paper deals with statistical inference for the scale mixture models. We study an estimation approach based on the Mellin -- Stieltjes transform that can be applied to both discrete and absolute continuous mixing distributions. The accuracy of the corresponding estimate is analysed in terms of its expected pointwise error. As an important technical result, we prove the analogue of the Berry -- Esseen inequality for the Mellin transforms. The proposed statistical approach is illustrated by numerical examples.

翻译：本文研究尺度混合模型的统计推断问题。我们探讨了一种基于梅林-斯蒂尔杰斯变换的估计方法，该方法可同时适用于离散型和绝对连续型混合分布。通过期望逐点误差分析了相应估计的精度。作为一项关键技术成果，我们证明了梅林变换的贝里-埃森不等式类似形式。通过数值算例对所提出的统计方法进行了验证。