Tales from the tail: Robust estimation of moments of environmental data with one-sided detection limits

Estimating the means and standard deviations of environmental data remains a great challenge because a substantial percentage of observations lies below or above detection limits. The inadequacy of several common, ad hoc estimation procedures is clear; this study instead proposes a robust moment estimation procedure for environmental data with a one-sided detection limit. The procedure assumes that the tails of the underlying distribution of the (transformed) data are symmetric, and censoring only occurs on one side. Through an application of the Rényi representation theorem, it is possible to use observations from the other side to learn the shape of the distribution below the detection limit, without specifying any particular parametric model, and consequently, derive the moment estimates of the distribution. A simulation provides a comparison of estimation performance between the proposed procedure and several existing estimators, and several real-life samples offer a good illustration.

► We propose a robust moment estimator for environmental data subject to a one-sided detection limit.
► The estimator is robust with respect to a class of tail-symmetric distributions.
► The estimator outperforms extant estimators with stronger distributional assumptions.
► We illustrate the use of the estimator with several real-life environmental samples.