We investigate algorithmic questions that arise in the statistical problem of computing lines or hyperplanes of maximum regression depth among a set of n points. We work primarily with a dual representation and find points of maximum undirected depth in an arrangement of lines or hyperplanes. An O(nd) time and space algorithm computes directed depth of all points in d dimensions. Properties of undirected depth lead to an O(n log2 n) time and O(n) space algorithm for computing a point of maximum depth in two dimensions. We also give approximation algorithms for hyperplane arrangements and degenerate line arrangements.
|Number of pages||10|
|State||Published - 1999|
|Event||Proceedings of the 1999 15th Annual Symposium on Computational Geometry - Miami Beach, FL, USA|
Duration: 13 Jun 1999 → 16 Jun 1999
|Conference||Proceedings of the 1999 15th Annual Symposium on Computational Geometry|
|City||Miami Beach, FL, USA|
|Period||13/06/99 → 16/06/99|