Estimating the probability mass of unobserved support in random sampling

A. Almudevar, R. N. Bhattacharya, C. C.A. Sastri

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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 languageEnglish (US)
Pages (from-to)91-105
Number of pages15
JournalJournal of Statistical Planning and Inference
Volume91
Issue number1
DOIs
StatePublished - Nov 1 2000

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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