On Improving Kernel Estimators Using Line Transect Sampling

Abstract

ABSTRACT We investigate some possibilities for improvements of kernel density estimates using line transect sampling. A bias correction approach is used which produces a new estimator for density of object D. The asymptotic bias of kernel estimator is subtracted from the kernel estimator to form the proposed estimator. It reduced the bias from O(h 2) to O(h 3) as h → 0 under the shoulder condition assumption and in some cases the bias reduced to O(h 4). The asymptotic theoretical properties of the proposed estimator are presented and the optimal formula for the bandwidth parameter h is given based on minimizing the asymptotic mean square error (AMSE). Moreover, in the absence of our knowledge whether or not the shoulder condition is valid another estimator is suggested, small-sample properties of the proposed estimators are studied and compared with some existing estimators by simulation technique. The results show the superiority of the proposed estimators among the other estimators for most cases considered.