Quantile contours and multivariate density estimation for massive datasets via sequential convex hull peeling

We propose a low-storage, single-pass, sequential method for the execution of convex hull peeling for massive datasets. The method is shown to vastly reduce the computation time required for the existing convex hull peeling algorithm from O(n²) to O(n). Furthermore, the proposed method has significantly smaller storage requirements compared to the existing method. We present algorithms for low-storage, sequential computation of both the convex hull peeling multivariate median and the convex hull peeling pth depth contour, where 0 > p > 1. We demonstrate the accuracy and reduced computation time required of the proposed method by comparing to the existing convex hull peeling method through simulation studies.