Abstract
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.
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