A non-parametric density estimate adaptation for population abundance when the shoulder condition is violated

The non-parametric kernel density estimation is used in practice to estimate population abundance using the line transect sampling. In general, the classical kernel estimator of f(0) tends to be underestimated. In this article, a shifted logarithmic transformation of perpendicular distance is proposed for the kernel estimator when the shoulder condition is violated. Mathematically, the proposed estimator is more efficient than the classical kernel estimator. A simulation study is also carried out to compare the performance of the proposed estimators and the classical kernel estimators.