On the Uniformly Most Powerful Invariant Test for the Shoulder Condition in Line Transect Sampling

In wildlife population studies one of the main goals is estimating the population abundance. Line transect sampling is a well established methodology for this purpose. The usual approach for estimating the density or the size of the population of interest is to assume a particular model for the detection function (the conditional probability of detecting an animal given that it is at a given distance from the observer). Two common models for this function are the half-normal model and the negative exponential model. The estimates are extremely sensitive to the shape of the detection function, particularly to the so-called shoulder condition, which ensures that an animal is almost certain to be detected if it is at a small distance from the observer. The half-normal model satisfies this condition whereas the negative exponential does not. Therefore, testing whether such a hypothesis is consistent with the data is a primary concern in every study aiming at estimating animal abundance. In this paper we propose a test for this purpose. This is the uniformly most powerful test in the class of the scale invariant tests. The asymptotic distribution of the test statistic is worked out by utilising both the half-normal and negative exponential model while the critical values and the power are tabulated via Monte Carlo simulations for small samples. .