文章基本信息

标题：A Good-Turing estimator for feature allocation models
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作者：Fadhel Ayed ; Marco Battiston ; Federico Camerlenghi 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2019
卷号：13
期号：2
页码：3775-3804
DOI：10.1214/19-EJS1614
语种：English
出版社：Institute of Mathematical Statistics
摘要：Feature allocation models generalize classical species sampling models by allowing every observation to belong to more than one species, now called features. Under the popular Bernoulli product model for feature allocation, we assume $n$ observable samples and we consider the problem of estimating the expected number $M_{n}$ of hitherto unseen features that would be observed if one additional individual was sampled. The interest in estimating $M_{n}$ is motivated by numerous applied problems where the sampling procedure is expensive, in terms of time and/or financial resources allocated, and further samples can be only motivated by the possibility of recording new unobserved features. We consider a nonparametric estimator $\hat{M}_{n}$ of $M_{n}$ which has the same analytic form of the popular Good-Turing estimator of the missing mass in the context of species sampling models. We show that $\hat{M}_{n}$ admits a natural interpretation both as a jackknife estimator and as a nonparametric empirical Bayes estimator. Furthermore, we give provable guarantees for the performance of $\hat{M}_{n}$ in terms of minimax rate optimality, and we provide with an interesting connection between $\hat{M}_{n}$ and the Good-Turing estimator for species sampling. Finally, we derive non-asymptotic confidence intervals for $\hat{M}_{n}$, which are easily computable and do not rely on any asymptotic approximation. Our approach is illustrated with synthetic data and SNP data from the ENCODE sequencing genome project.
关键词：Bernoulli product model; feature allocation model; Good-Turing estimator; minimax rate optimality; missing mass; non-asymptotic uncertainty quantification; nonparametric empirical Bayes; SNP data