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

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