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Estimating the number of classes in multiple populations: A geometric analysis
Author(s) -
Mao Chang Xuan,
Lindsay Bruce G.
Publication year - 2004
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315931
Subject(s) - confidence interval , multivariate statistics , inference , statistics , mathematics , poisson distribution , nonparametric statistics , class (philosophy) , point estimation , odds , point (geometry) , multivariate analysis , computer science , logistic regression , artificial intelligence , geometry
The authors study estimation of the total number of classes present in multiple overlapping populations. They show that the number of classes is identifiable in a nonparametric mixture model of multivariate Poisson densities. Unusual phenomena occur in both point estimation and confidence inference for the parameter defined as the odds of a class being unidentified in the data. Consequently only one‐sided confidence intervals are available for the number of classes.