### Abstract

The problem of estimating the probability mass of the support of a distribution not observed in random sampling is considered in the case where the distribution is discrete. An example of a situation in which the problem arises is that of species sampling: suppose that one wishes to determine the species of fish native to a body of water and that, after repeated sampling, one identifies a certain number of species. The problem is to estimate the proportion of the fish population belonging to the unobserved species. Since it is a rare event, ideas from large deviation theory play a role in answering the question. The result depends on the underlying distribution, which is unknown in general. Methods similar to nonparametric bootstrapping are therefore used to prove a limit theorem and obtain a confidence interval for the rate function.

Original language | English (US) |
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Pages (from-to) | 91-105 |

Number of pages | 15 |

Journal | Journal of Statistical Planning and Inference |

Volume | 91 |

Issue number | 1 |

State | Published - Nov 1 2000 |

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### Keywords

- Bootstrapping
- Large deviations
- Primary 62E20
- Secondary 60F10
- Unobserved support

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics

### Cite this

*Journal of Statistical Planning and Inference*,

*91*(1), 91-105.