title: Mathematical models for nonparametric inferences from line transect data.
abstract: A general mathematical theory of line transects is develoepd which supplies a framework for nonparametric density estimation based on either right angle or sighting distances. The probability of observing a point given its right angle distance (y) from the line is generalized to an arbitrary function g(y). Given only that g(O) = 1, it is shown there are nonparametric approaches to density estimation using the observed right angle distances. The model is then generalized to include sighting distances (r). Let f(y/r) be the conditional distribution of right angle distance given sighting distance. It is shown that nonparametric estimation based only on sighting distances requires we know the transformation of r given by f(O/r).
mesh_terms: D000818:Animals; D001699:Biometry; D001717:Birds / Q000502:physiology; D008954:Models, Biological; D011156:Population Density; D013223:Statistics as Topic