Asymptotic Unbiased Kernel Estimator for Line Transect Sampling

Abstract

In this article, we propose a new estimator for the density of objects using line transect data. The proposed estimator combines the nonparametric kernel estimator with parametric detection function: the exponential or the half normal detection function to estimate the density of objects. The selection of the detection function depends on the testing of the shoulder condition assumption. If the shoulder condition is true then the half-normal detection function is introduced together with the kernel estimator. Otherwise, the negative exponential is combined with the kernel estimator. Under these assumptions, the proposed estimator is asymptotically unbiased and it is strongly consistent estimator for the density of objects using line transect data. The simulation results indicate that the proposed estimator is very successful in taking the advantage of the parametric detection function available.

Keywords:

• Dominated convergence theorem
• Half-normal model
• Kernel method
• Line transect method
• Negative exponential model

Mathematics Subject Classification:

• Primary 62D05
• Secondary 62L12