Inference of distributional parameters from compositional samples containing nondetects
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Low concentrations of elements in geochemical analyses have the peculiarity of being
compositional data and, for a given level of significance, are likely to be beyond the
capabilities of laboratories to distinguish between minute concentrations and complete
absence, thus preventing laboratories from reporting extremely low concentrations of the
analyte. Instead, what is reported is the detection limit, which is the minimum
concentration that conclusively differentiates between presence and absence of the
element. A spatially distributed exhaustive sample is employed in this study to generate
unbiased sub-samples, which are further censored to observe the effect that different
detection limits and sample sizes have on the inference of population distributions
starting from geochemical analyses having specimens below detection limit (nondetects).
The isometric logratio transformation is used to convert the compositional data in the
simplex to samples in real space, thus allowing the practitioner to properly borrow from
the large source of statistical techniques valid only in real space. The bootstrap method is
used to numerically investigate the reliability of inferring several distributional
parameters employing different forms of imputation for the censored data. The case
study illustrates that, in general, best results are obtained when imputations are made
using the distribution best fitting the readings above detection limit and exposes the
problems of other more widely used practices. When the sample is spatially correlated, it
is necessary to combine the bootstrap with stochastic simulation
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