偏态自适型投影深度

A Skewness-Adaptive Projection Depth

对常规投影深度进行了改进,得到了一类新的可自适应反映多元数据云偏态的统计投影深度.新的深度函数仍然具有凸的深度域,满足一般统计深度函数所应具备的全部基本特点.此外,还考虑了新投影深度函数的计算问题,证得在任意维空间里,它及由它诱导的深度域均是可以精确计算的,从技术角度讲,其处理比常规投影深度更加简便.最后,提供了一些数据示例用以展示此偏态自适型投影深度的有限样本性质.

This paper extends the usual projection depth to a version adjusted for possible skewness in the data cloud.The proposal has convex depth regions,and satisfies all the properties of a general statistical depth function.Its computing issue is also investigated.It is shown that the exact computation of the proposal,as well as the related depth regions,is still possible in any dimension,and technically much simpler to be implemented than the usual projection depth.Finally,data examples are provided to illustrate the finite sample performance of this skewness-adaptive projection depth.