On the uniformly most powerful invariant test for the shoulder condition in line transect sampling
| STATISTICA & APPLICAZIONI - 2009 - 1
In wildlife population studies one of the main goals is estimating the population density. Line transect
sampling is a well established methodology for this purpose. The usual approach for estimating
the density of the population of interest is to assume a particular model for the detection function.
The estimates are extremely sensitive to the shape of the detection function, particularly to the socalled
shoulder condition, which ensures that an animal is nearly certain to be detected if it is at a
small distance from the observer. For instance, the half-normal model satisfies this condition
whereas the negative exponential does not. So, testing whether the shoulder condition is consistent
with the data is a primary concern. Since the problem of testing such a hypothesis is invariant under
the group of scale transformations, in this paper we propose the uniformly most powerful test
in the class of the scale invariant tests for the half-normal model against the negative exponential
model. The asymptotic distribution of the test statistic is derived. The critical values and the power
are tabulated via Monte Carlo simulations for small samples.