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Biometrika 1993 80(4):797-806; doi:10.1093/biomet/80.4.797
© 1993 by Biometrika Trust
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Optimal estimation under biased allocation of treatments

V. P. GODAMBE1 and S. KUNTE2

1Department of Statistics and Actuarial Science, University of Waterloo Waterloo, Ontario, N2L 3G1, Canada
2Department of Statistics, University of Poona Pune-411007, India

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 investigated in this paper, the efficiency of our estimation appears very close to that of maximum likelihood estimation.

Key Words: Biased allocation • Efficiency • Estimating functions • Optimality • Posterior mean


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