Optimal estimation under biased allocation of treatments

SUMMARY This paper provides a semi-parametric solution to a problem proposed by Robbins & Zhang (1991). The solution is obtained utilizing the theory of optimum estimating functions (Godambe & Thompson, 1989). Our solution coincides with maximum likelihood estimation for the parametric model suggested by Robbins & Zhang (1991). Even for alternative models investigted in this paper, the efficiency of our estimation appears very close to that of maximum likelihood estimation.