Bias reduction and efficiency of reconstructed ratio estimators for a finite universe

Summary The bias of ratio estimators based on a simple random sample ofn units drawn from a finite universe ofN units, and reconstructed according to, or in ways similar to Quenouille's method, is of order 1/n only ifN≧n ², and of order 1/n ^Q , where 1<Q<2, ifN<n ². Further it is shown that the device of splitting samples, either for bias reduction and/or convenience of variance estimation, except for the special case noted in the paper, yields estimators that are inefficient and can be improved.