Kernel Method Starting with Half-Normal Detection Function for Line Transect Density Estimation

Abstract

In this article, we introduce the nonparametric kernel method starting with half-normal detection function using line transect sampling. The new method improves bias from O(h 2), as the smoothing parameter h → 0, to O(h 3) and in some cases to O(h 4). Properties of the proposed estimator are derived and an expression for the asymptotic mean square error (AMSE) of the estimator is given. Minimization of the AMSE leads to an explicit formula for an optimal choice of the smoothing parameter. Small-sample properties of the estimator are investigated and compared with the traditional kernel estimator by using simulation technique. A numerical results show that improvements over the traditional kernel estimator often can be realized even when the true detection function is far from the half-normal detection function.