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Estimation of the number of species or unobserved classes from a randomsample of the underlying population is a ubiquitous problem in statistics. Inclassical settings, the size of the sample is usually small. New technologiessuch as high-throughput DNA sequencing have allowed for the sampling ofextremely large and heterogeneous populations at scales not previouslyattainable or even considered. New algorithms are required that take advantageof the size of the data to account for heterogeneity, but are also sufficientlyfast and scale well with large data. We present a non-parametric moment-basedestimator that is both computationally efficient and is sufficiently flexibleto account for heterogeneity in the abundances of underlying population. Thisestimator is based on an extension of a popular moment-based lower bound (Chao,1984), originally developed by Harris (1959) but unattainable due to the lackof economical algorithms to solve the system of nonlinear equation required forestimation. We apply results from the classical moment problem to show thatsolutions can be obtained efficiently, allowing for estimators that aresimultaneously conservative and use more information. This is critical formodern genomic applications, where there may be many large experiments thatrequire the application of species estimation. We present applications of ourestimator to estimating T-Cell receptor repertoire and dropout in single cellRNA-seq experiments.

Better lower bounds for missing species: improved non-parametric moment-based estimation for large experiments