S.A. Patil | Search USGS

USGS1982

Optimum nonparametric estimation of population density based on ordered distances

The asymptotic mean and error mean square are determined for the nonparametric estimator of plant density by distance sampling proposed by Patil, Burnham and Kovner (1979, Biometrics 35 , 597-604. On the basis of these formulae, a bias-reduced version of this estimator is given, and its specific form is determined which gives minimum mean square error under varying assumptions about the true probability density function of the sampled data. Extension is given to line-transect sampling.

Biometrics↗

USGS1979

Nonparametric estimation of plant density by the distance method

A relation between the plant density and the probability density function of the nearest neighbor distance (squared) from a random point is established under fairly broad conditions. Based upon this relationship, a nonparametric estimator for the plant density is developed and presented in terms of order statistics. Consistency and asymptotic normality of the estimator are discussed. An interval estimator for the density is obtained. The modifications of this estimator and its variance are given when the distribution is truncated. Simulation results are presented for regular, random and aggregated populations to illustrate the nonparametric estimator and its variance. A numerical example from field data is given. Merits and deficiencies of the estimator are discussed with regard to its robustness and variance.

Biometrics↗