Structural properties and convergence results for contours of sample statistical depth functions
研究了统计深度函数轮廓的结构性质，如仿射等变性、嵌套性、连通性和紧致性，并证明了样本深度轮廓的几乎必然收敛结果，对多元非参数推断有重要参考价值。
Statistical depth functions have become increasingly used in nonparametric inference for multivariate data. Here the contours of such functions are studied. Structural properties of the regions enclosed by contours, such as affine equivariance, nestedness, connectedness and compactness, and almost sure convergence results for sample depth contours, are established. Also, specialized results are established for some popular depth functions, includinghalfspace depth, and for the case of elliptical distributions. Finally, some needed foundational results on almost sure convergence of sample depth functions are provided.