Simultaneous Estimation of Multinomial Cell Probabilities. Fienberg, S. E. & Holland, P. W. *Journal of the American Statistical Association*, 68(343):683–691, September, 1973. doi abstract bibtex A new estimator, p*, of the multinomial parameter vector is proposed, and it is shown to be a better choice in most situations than the usual estimator, (the vector of observed proportions). The risk functions (expected squared-error loss) of these two estimators are examined in three ways using: (a) exact calculations, (b) standard asymptotic theory, and (c) a novel asymptotic framework in which the number of cells is large and the number of observations per cell is moderate. The general superiority of p* over in large sparse multinomials is thus revealed. The novel asymptotic framework may also provide insight in other multinomial problems.

@article{fienbergSimultaneousEstimationMultinomial1973,
title = {Simultaneous Estimation of Multinomial Cell Probabilities},
author = {Fienberg, Stephen E. and Holland, Paul W.},
year = {1973},
month = sep,
volume = {68},
pages = {683--691},
issn = {1537-274X},
doi = {10.1080/01621459.1973.10481405},
abstract = {A new estimator, p*, of the multinomial parameter vector is proposed, and it is shown to be a better choice in most situations than the usual estimator, (the vector of observed proportions). The risk functions (expected squared-error loss) of these two estimators are examined in three ways using: (a) exact calculations, (b) standard asymptotic theory, and (c) a novel asymptotic framework in which the number of cells is large and the number of observations per cell is moderate. The general superiority of p* over in large sparse multinomials is thus revealed. The novel asymptotic framework may also provide insight in other multinomial problems.},
journal = {Journal of the American Statistical Association},
keywords = {*imported-from-citeulike-INRMM,~INRMM-MiD:c-14064644,~to-add-doi-URL,bias-correction,confusion-matrix,presence-absence,statistics},
lccn = {INRMM-MiD:c-14064644},
number = {343}
}

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