Burnham K P, Anderson D R
Biometrics. 1976 Jun;32(2):325-36.
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).
发展了一种线截线的通用数学理论，该理论为基于直角距离或观测距离的非参数密度估计提供了一个框架。给定一个点到直线的直角距离（y），观察到该点的概率被推广为一个任意函数g(y)。仅给定g(0)=1，结果表明存在使用观测到的直角距离进行密度估计的非参数方法。然后该模型被推广到包括观测距离（r）。设f(y/r)为给定观测距离时直角距离的条件分布。结果表明，仅基于观测距离的非参数估计要求我们知道由f(0/r)给出的r的变换。
