An improved transformation-based kernel estimator for population abundance with shoulder condition

The estimation of parameter integral(X)(0), which is the probability density function at the perpendicular distance x = 0, is a common target in the line transect sampling to estimate the population abundance, D. The key assumption of the density shape in the line transect sampling is known as the shoulder condition (f(X)'(0) = 0). In this paper, we propose a log-transformation application as an adaptation of the classical kernel method to estimate the population abundance in the line transect sampling. The proposed transformation produces a simple and interpretable estimator as the usual kernel estimator while holding theoretical and practical advantages. The asymptotic properties of the proposed transformation are derived. A simulation study using the half-normal detection function is also investigated and applied using various sample sizes. Theoretical and practical results show the superior potential properties of the proposed transform estimator over the usual kernel estimator.