Studying school size effects in line transect sampling using the kernel method

When conducting line transect sampling to estimate the abundance of a clustered wildlife population, detection of a school depends not only on the perpendicular distance of the school to the transect line, but also on the size of school. Larger size schools are easier to detect than smaller schools. Thus, a bivariate detection function with distance and size as covariates should be considered. This paper considers using the kernel smoothing method to fit the bivariate line transect data in order to estimate both abundance and the mean school size. Two kernel estimators are studied: the fixed kernel estimator, which uses the same smoothing bandwidth for all data points, and the adaptive kernel estimator, which allows the bandwidth to vary across the data points.