Estimating the probability mass of unobserved support in random sampling

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 sp...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2000-11, Vol.91 (1), p.91-105
Main Authors: Almudevar, A., Bhattacharya, R.N., Sastri, C.C.A.
Format: Article
Language:English
Subjects:
Bootstrapping
Distribution theory
Exact sciences and technology
Large deviations
Limit theorems
Mathematics
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Statistics
Unobserved support
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Summary: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.
ISSN:0378-3758
1873-1171
DOI:10.1016/S0378-3758(00)00125-7