Estimation of averages in truncated samples

This paper compares methodologies for the estimation of the mean of a series of observations that contain results below a known detection limit. The bias-corrected restricted maximum likelihood method, not previously employed in environmental science and engineering, is found to be the least biased estimator, with a mean square error only slightly greater than the ordinary maximum likelihood method. This method is more robust to a variety of deviations from normality and, in particular, is better than either graphical or half detection limit methods, in most cases. It is also somewhat easier to compute than the maximum likelihood method.