“…For fixed value of k, let (i) denotes the distance from w i ≡ (x i , y i , z i ) to its kth nearest neighbor, where distance is measured as the max-norm in the joint space, w i −w j xyz = max{ x i −x j x , y i −y j y , z i −z j z }, and the norms used in the subspaces can be arbitrary but often time the max norm is used (which is our choice for this paper) as well. From this we obtain • n xz (i): number of points (x j , z j ) ( j = i) with (x j , z j ) − (x i , z i ) xz = max{ x j − x i x , z j − z i z } < (i) • n yz (i): number of points (y j , z j ) ( j = i) with (y j , z j ) − (y i , z i ) yz = max{ y j − y i y , z j − z i z } < (i) • n z (i): number of points z j ( j = i) with z j − z i z < (i) Several recent papers have focused on reducing the finitesample bias of the KSG type of estimators [70]- [72] or developing other types of estimators [73].…”