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Optimal rate estimation of the mixing distribution in Poisson mixture models via Laplace inversion. (English) Zbl 1458.62128

Summary: Consistent estimators of the mixing distribution in Poisson mixture models are constructed for both the right censored and the uncensored case. The estimators are based on a kind of Laplace inversion via factorial moments. The rate of convergence of the mean integrated squared error of these estimators is \((\log n/\log \log n)^2\). It is also shown that there do not exist estimators for which this rate is better.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
62H12 Estimation in multivariate analysis
62N01 Censored data models
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
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