Results on double sample estimation for the binomial distribution
The authors consider a sequence of i.i.d. Bernoulli variables with parameter p, 0\(\leq p\leq 1\). A complete class result is obtained for double sample estimation and sequential estimation. The complete class result can be applied to prove that if the loss is a linear combination of squared error and cost of sampling then any estimation procedure (with its sampling rule) where the sample proportion is the terminal decision is inadmissible except for the case where the total sample is a single observation. If the terminal decision loss function is squared error divided by p(1-p) and the overall loss is a linear combination, then any double sample procedure in which the estimate is the sample proportion is inadmissible. These last two results demonstrate the inadmissibility of the Miller- Freund procedure for various linear combination loss functions. Finally, it is shown that the sample proportion as a true double sample estimate is not unbiased.
inadmissibility of the Miller-Freund procedure
scientific article; zbMATH DE number 3868450