Efficiency of presence‐absence sampling used to estimate the mean abundance of fish eggs

Statistical properties of estimators relating to the mean abundance of fish eggs were investigated using the data from the presence-absence sampling (PAS) and counting sampling (CS). PAS, which focuses on the presence-absence of eggs in a sample, is more cost-effective yet is unlikely to give more precise estimates than CS, which counts the number of eggs. But when limitations are given on the sampling cost and number of sampling stations, PAS may have advantages. This study shows that the mean square error (MSE) of the maximum likelihood estimator (MLE) based on PAS may become smaller than the MSE of the MLE based on counting data when the number of observations for PAS becomes larger. The observation number for PAS is determined, which minimizes the MSE of a combined estimator from the two MLE under a restriction of the total cost of observation. A dual problem is also solved. It is shown that MSE of the MLE in PAS is a monotone increasing function of the oversight probability. PAS becomes more informative as the distribution of the number of eggs is more aggregated.