Pooling the perpendicular distances from two or more line transects to estimate the population abundance is often used by researchers. Instead of pooling the data, this paper focuses in combining the estimators resulting from different line transects in a single estimator with some weights. The nonparametric fourth-order kernel method is considered for this purpose and the corresponding weights are determined by minimizing the variance of the resulting estimator for both cases; when the detection functions are assumed to be the same and when they are assumed to be different. The asymptotic properties of the proposed estimator are derived. The numerical results of this paper show that some improvements can be obtained when the estimators are combined instead of pooling the data.

line transect method, shoulder condition, population abundance, fourth-order kernel method, asymptotic mean square error and smoothing parameter.