Kernel estimation in transect sampiing withoyt the shoulder condition

Abstract

We consider the estiinution of wildlife population density based on line transect data. Nonparametric kernel method is employed, without the usual assumption that the detection curve has a shoulder at distance zero, with the help of a special class of kernels called boundary kernels. Asymptotic distribution results are included. It is pointed out that the boundery kernel of Zhang and Karunamuni (1998) (see also Müller and Wang (1994)) performs better (for asmyptotic mean square error consideration) than that of the boundary kernel of M¨ller (1991). But both of these kernels are clearly superior to the half-nonnal and one-sided Epanechnikov kernel when the shoulder condition fails to hold. In practice, however, for small to moderate sample sizes, caution should be exercised in using bounrlary kernels in that the density estimate might become negative. A Monte Carlo study is also presented, comparing the performance of four kernels applied to detection data, with and without the shoulder condition, Two bundary kernels for deriatives are also included for the point transect case.