ESTIMATING THE HOME-RANGE

A proposal is given for estimating the home range of an animal based on sequential sightings. We assume the given sightings are independent, identically distributed random vectors X1, ..., X(n) whose common distribution has compact support. If {(R(i), THETA(i), 1 less-than-or-equal-to i less-than-or-equal-to n} are the polar coordinates of the sightings, then l(v)(I) = sup {x: P[R1 > x, THETA1 is-an-element-of I] > 0} is a sup-measure and corresponds to the right endpoint of the distribution P[R1 less-than-or-equal-to x / THETA1 is-an-element-of I]. The corresponding upper semi-continuous function l (theta) is the boundary of the home range. We give a consistent estimator for the boundary l and under the assumption that the distribution of R1 given THETA1 is-an-element-of I is in the domain of attraction of an extreme value distribution with bounded support, we are able to give an approximate confidence region.