Uniformly most powerful unbiased test for shoulder condition in point transect sampling

Point transect sampling is a well-known methodology for estimating wildlife population density. In this context, the usual approach is to assume a model for the detection function. Thus, the estimate depends on the shape of the detection function. In particular, the estimation is influenced by the so-called shoulder condition, which guarantees that detection is nearly certain at small distances from the observer. For instance, the half-normal model satisfies this condition, whereas the negative exponential model does not. Testing whether the shoulder condition is consistent with data is a crucial issue. In this paper we propose the uniformly most powerful unbiased test for the shoulder condition in the exponential mixture model of the half-normal and the negative exponential. Critical values of the proposed test are calculated for large samples by means of asymptotic distribution theory and for small samples via Monte Carlo simulations. Finally, a case study is presented. Copyright Springer-Verlag 2012