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Estimating the Binomial Parameter N on the Basis of Pairs of Known and Observed Proportions
Author(s) -
O'Quigley John
Publication year - 1992
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.2307/2347626
Subject(s) - binomial (polynomial) , basis (linear algebra) , mathematics , statistics , binomial coefficient , econometrics , combinatorics , geometry
SUMMARY We consider estimation of the parameter n from a sequence of binomial trials, B ( n , p i ) , i = 1 , … , k . The observations consist of estimatesp ̂ iof the fixed and known parameters p i . The inferential problem concerns n which is unknown. Maximum likelihood estimates are derived as well as moment estimates. The applied problem motivating this work was that of estimating the number of stem cells involved in repopulating the marrow following allogeneic bone marrow transplantation. An estimator, popular with applied workers in this field, is seen to be a moment estimator. its statistical properties are poor and its use should be discouraged. An alternative moment estimator is derived and behaves similarly to the maximum likelihood estimator. We rework data gathered to address the issue of marrow repopulation to illustrate the techniques proposed. A comparison of estimators is also provided.