Better lower bounds for missing species: improved non-parametric   moment-based estimation for large experiments
  Estimation of the number of species or unobserved classes from a random sample of the underlying population is a ubiquitous problem in statistics. In classical settings, the size of the sample is usually small. New technologies such as high-throughput DNA sequencing have allowed for the sampling of extremely large and heterogeneous populations at scales not previously attainable or even considered. New algorithms are required that take advantage of the size of the data to account for heterogeneity, but are also sufficiently fast and scale well with large data. We present a non-parametric moment-based estimator that is both computationally efficient and is sufficiently flexible to account for heterogeneity in the abundances of underlying population. This estimator is based on an extension of a popular moment-based lower bound (Chao, 1984), originally developed by Harris (1959) but unattainable due to the lack of economical algorithms to solve the system of nonlinear equation required for estimation. We apply results from the classical moment problem to show that solutions can be obtained efficiently, allowing for estimators that are simultaneously conservative and use more information. This is critical for modern genomic applications, where there may be many large experiments that require the application of species estimation. We present applications of our estimator to estimating T-Cell receptor repertoire and dropout in single cell RNA-seq experiments. 
Timothy Daley and Andrew D Smith
stat.ME q-bio.QM