Admissible test for shoulder condition in line transect sampling under an exponential mixture model

Line transect sampling is a distance sampling method widely used for estimating wildlife population density. Since the usual approach assumes a model for the detection function, the estimate depends on the shape of such a function. In particular, the estimate is influenced by the so-called shoulder condition, which ensures that detection is nearly certain at small distances from the line transect. For instance, the halfnormal model satisfies this condition, whereas the negative exponential model does not. So, testing whether the shoulder condition is consistent with the data represents a fundamental issue. The aim of this paper is to propose an admissible test for the shoulder condition in the exponential mixture model of the half-normal and the negative exponential. Critical value and p-value of the proposed test are calculated by means of asymptotic distribution theory.