Local parametric density estimation methods in line transect sampling

A semiparametric estimator of animal abundance based on local parametric density estimation is considered in line transect sampling. A key parametric model is initially assumed for the observed perpendicular distances and its parameters are estimated on the basis of standard likelihood methods. Subsequently, the estimation is nonparametrically corrected by using a local kernel-smoothed criterion function. In this case, the kernel bandwidth controls the amount of smoothing to be applied to the estimator, in the sense that large bandwidths are to be used if the key model is properly selected, while with small bandwidths the choice of the key parametric model is non-influential. The method provides consistent estimation, whatever key parametric model is chosen, and it improves over the purely nonparametric kernel estimation, since it takes into account that the probability density function of the observed distances is monotone decreasing and the so-called "shoulder" condition is often true. The results of a Monte Carlo study suggest that the proposed method performs very well with respect to the existing nonparametric and semiparametric estimators.