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Consistent Estimation of the Structural Distribution Function

Chris A. J. Klaassen and Robert M. Mnatsakanov
Scandinavian Journal of Statistics
Vol. 27, No. 4 (Dec., 2000), pp. 733-746
Stable URL: http://www.jstor.org/stable/4616638
Page Count: 14
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Consistent Estimation of the Structural Distribution Function
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Abstract

Motivated by problems in linguistics we consider a multinomial random vector for which the number of cells N is not much smaller than the sum of the cell frequencies, i.e. the sample size n. The distribution function of the uniform distribution on the set of all cell probabilities multiplied by N is called the structural distribution function of the cell probabilities. Conditions are given that guarantee that the structural distribution function can be estimated consistently as n increases indefinitely although n/N does not. The natural estimator is inconsistent and we prove consistency of essentially two alternative estimators.

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