Local bandwidth selection for kernel estimation of population densities with line transect sampling.

Seber (1986, Biometrics 42, 267-292) suggested an approach to biological population density estimation using kernel estimates of the probability density of detection distances in line transect sampling. Chen (1996a, Applied Statistics 45, 135-150) and others have employed cross validation to choose a global bandwidth for the kernel estimator or have suggested adaptive kernel estimation (Chen, 1996b, Biometrics 52, 1283-1294). Because estimation of the density is required at only a single point, we investigate a local bandwidth selection procedure that is a modification of the method of Schucany (1995, Journal of the American Statistical Association 90, 535-540) for nonparametric regression. We report on simulation results comparing the proposed method and a local normal scale rule with cross validation and adaptive estimation. The local bandwidths and normal scale rule produce estimates with mean squares that are half the size of the others in most cases. Consistency results are also provided.