Abstract
Suppose that X has a binomial distribution B(n,p), with known p∈(0,1) and unknown n∈{1,2,⋯}. A natural estimator for n is given by T(0)=1,T(x)=x/p,x=1,2,⋯. This estimator is shown to be inadmissible under quadratic loss. It is shown that modifying T(0) to T(0)=−(1−p)/(plnp) results in an admissible estimator. For p≥12 it is further shown that this is the only admissible modification of T(0). A partial result is also obtained for p<12.
Citation
S. M. Sadooghi-Alvandi. "Admissible Estimation of the Binomial Parameter n." Ann. Statist. 14 (4) 1634 - 1641, December, 1986. https://doi.org/10.1214/aos/1176350185
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