Online bootstrap inference for the geometric median

Abstract

In real-world applications, the geometric median is a natural quantity to consider for robust inference of location or central tendency, particularly when dealing with non-standard or irregular data distributions. An innovative online bootstrap inference algorithm, using the averaged nonlinear stochastic gradient algorithm, is proposed to make statistical inference about the geometric median from massive datasets. The method is computationally fast and memory-friendly, and it is easy to update as new data is received sequentially. The validity of the proposed online bootstrap inference is theoretically justified. Simulation studies under a variety of scenarios are conducted to demonstrate its effectiveness and efficiency in terms of computation speed and memory usage. Additionally, the online inference procedure is applied to a large publicly available dataset for skin segmentation.