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

3 Estimating the means and standard deviations of environmental data remains a great chal4 lenge because a substantial percentage of observations lies below or above detection limits. 5 The inadequacy of several common, ad hoc estimation procedures is clear; this study instead 6 proposes a robust moment estimation procedure for environmental data with a one-sided 7 detection limit. The procedure assumes that the tails of the underlying distribution of the 8 (transformed) data are symmetric, and censoring only occurs on one side. Through an 9 application of the Rényi representation theorem, it is possible to use observations from the 10 other side to learn the shape of the distribution below the detection limit, without speci11 fying any particular parametric model, and consequently, derive the moment estimates of 12 the distribution. A simulation provides a comparison of estimation performance between 13 the proposed procedure and several existing estimators, and several real-life samples offer 14 a good illustration. 15 16