Abstract: In this paper, we
introduce a nonparametric fourth-order kernel method for line transect sampling.
This method produces a new estimator for the densityof objects using line transect data. The asymptotic properties of the
proposed estimator are derived under some mild assumptions. Moreover, an
explicit formula for the smoothing parameter h
is obtained based on minimizing the asymptotic mean square error (AMSE).
Further, another estimator is suggested when there is no information whether the
shoulder conditionis valid or
not. The performances of the proposed estimators are studied and compared with
some existing estimators by simulation technique. As the results demonstrated,
the fourth-order kernel method has overall better performance than the
traditional kernel method, and in many cases is much more effective.
Keywords and phrases: line transect method, shoulder condition, fourth-order kernel method.
