Transposed conditionals, shrinkage, and direct and indirect unbiasedness

Abstract

Unbiasedness as conventionally understood is not a necessary property of good inferences. Such unbiasedness is "direct"--it guarantees that, on average, an estimate equals the thing it is estimating (the parameter). Strange as it may seem, this does not mean that the parameter is on average equal to its estimate. This would require the very different property of inverse unbiasedness. When this phenomenon is understood, shrinkage of results can be seen to be a necessary fact of life.