  The relative abundances of species in a microbiome is a scientifically
important parameter to estimate given the critical role that microbiomes play
in human and environmental health. However, data from artificially constructed
microbiomes shows that measurement error may induce substantial bias in common
estimators of this quantity. To address this, we propose a semiparametric model
that accounts for common forms of measurement error in microbiome experiments.
Notably, our model allows relative abundances to lie on the boundary of the
simplex. We present a stable algorithm for computing parameter estimates,
asymptotically valid procedures for inference in this nonstandard problem, and
examples of the utility of the method. Our approach can be used to select or
compare experimental protocols, design experiments with appropriate control
data, analyze mixed-specimen samples, and remove across-sample contamination.
