The convex hull of a dependent vector-valued process

Abstract

An important problem in the study of animal behaviour is the determination of home range. This set can be estimated by the convex hull of the location of an animal at successive time points. However, this estimate is based on a sample of highly dependent observations when the time intervals between fixes are small. In this paper we quantify the effect of dependence on various properties of the convex hull of several dependent point processes in the plane using Monte-Carlo methods. We compare our results with the independent case and make some comments on the asymptotic behaviour of this set.

Keywords:

• Convex hull
• dependent point process
• area
• perimeter length
• shape
• Monte-Carlo
• home range