A Consistent Estimator of Structural Distribution
We consider sparse count data models with the sparsity rate τ = N/n = O(1) where N = N (n) is the number of observations and n → ∞ is the number of cells. In this case the plug-in estimator of the structural distribution of expected frequencies is inconsistent. If τ = O(n −α ) for some α > 0, the nonparametric maximum likelihood estimator, in general, is also inconsistent. Assuming that some auxiliary information on the expected frequencies is available, we construct a consistent estimator of the structural distribution.
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