Does this have some connection to the unbiased/maximal likelihood estimator dichotomy?
I don’t really have a clear picture, so this should be treated only as a vague intution that someone could hopefully formalize, but I feel that somehow the maximal likelihood estimator would be in the 1⁄3 camp, since it optimizes just for the payoff—and, on the other hand, unbiased estimator would be in the 1⁄2 camp, since it optimizes for accuracy. Then, the whole problem comes down to the well-known issue that in some cases, MLE are not unbiased (e.g. classic problem with variance estimator).
Does this have some connection to the unbiased/maximal likelihood estimator dichotomy?
I don’t really have a clear picture, so this should be treated only as a vague intution that someone could hopefully formalize, but I feel that somehow the maximal likelihood estimator would be in the 1⁄3 camp, since it optimizes just for the payoff—and, on the other hand, unbiased estimator would be in the 1⁄2 camp, since it optimizes for accuracy. Then, the whole problem comes down to the well-known issue that in some cases, MLE are not unbiased (e.g. classic problem with variance estimator).