This paper introduces several depths for random sets with possibly non-convex realisations, proposes ways to estimate the depths based on the samples and compares them with existing ones. The depths are further applied for the comparison between two samples of random sets using a visual method of DD-plots and statistical testing. The advantage of this approach is identifying sets within the sample that are responsible for rejecting the null hypothesis of equality in distribution and providing clues on differences between distributions. The method is justified using a simulation study and applied to real data consisting of histological images of mastopathy and mammary cancer tissue.

翻译：本文针对可能具有非凸实现的随机集引入了若干种深度，提出了基于样本估计深度的途径，并与已有深度进行了比较。进一步将这些深度应用于两组随机集之间的比较，采用了DD图的可视化方法和统计检验。该方法的优势在于能够识别出样本中导致零假设（分布相等）被拒绝的那些随机集，为分布差异提供线索。通过模拟研究验证了该方法的合理性，并将其应用于由乳腺病变组织与乳腺癌组织的组织学图像组成的实际数据。