On parametric estimation of population abundance for line transect sampling

Despite recent advances in nonparametric methods for estimating animal abundance, parametric methods are still used widely among biometricians due to their simplicity. In this paper, we propose an optimal shrinkage-type estimator and an empirical Bayes estimator for estimating animal density from line transect sampling data. The performances of the proposed estimators are compared with those of the maximum likelihood estimator and a bias-corrected maximum likelihood estimator both theoretically and numerically. Simulation results show that the optimal shrinkage-type estimator works the best if the detection function has a very thin tail (for example, the half normal detection function), while the maximum likelihood estimator is the best estimator if the detection function has relatively thick tail (for example, the polynomial detection function).