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Consistent Estimation of the Structural Distribution Function
Author(s) -
Klaassen Chris A. J.,
Mnatsakanov Robert M.
Publication year - 2000
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00219
Subject(s) - mathematics , multinomial distribution , estimator , consistency (knowledge bases) , distribution (mathematics) , function (biology) , distribution function , statistics , strong consistency , combinatorics , discrete mathematics , mathematical analysis , physics , quantum mechanics , evolutionary biology , biology
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.