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Estimating the Binomial Parameter N on the Basis of Pairs of Known and Observed Proportions

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  • John O'Quigley

Abstract

We consider estimation of the parameter n from a sequence of binomial trials, B(n,pi), i=1, …,k. The observations consist of estimates p̂i of the fixed and known parameters pi. 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.

Suggested Citation

  • John O'Quigley, 1992. "Estimating the Binomial Parameter N on the Basis of Pairs of Known and Observed Proportions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(1), pages 173-180, March.
    • Handle: RePEc:bla:jorssc:v:41:y:1992:i:1:p:173-180
    DOI: 10.2307/2347626
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