A new kernel estimator for abundance using line transect sampling without the shoulder condition

Estimation of the parameter f(0) (the probability density function at the left boundary x=0) is the key problem in line transect sampling to estimate the population abundance, D. The usual reflection kernel method is specially designed to estimate f(0) under the assumption that f(1)(0)=0, the first derivative of the probability density function at x=0 is zero. This assumption is known as the shoulder condition assumption in line transect sampling. This paper suggests a new adaptive version of the reflection kernel method to estimate f(0) when f(1)(0)≠0. The proposed method produces a class of estimators for f(0) which are as simple and interpretable as the usual reflection kernel estimator, while holding theoretical and practical advantages. The asymptotic properties of the proposed estimator are derived, and some important special cases of this estimator are investigated and studied. Theoretical and practical results show the good potential properties of the proposed estimator over the boundary kernel estimator.