On Efficiency of Small-Sample Estimates

In order to estimate the expectation of a function of random argument, we introduce a biased inconsistent pseudo-estimator, which is the same functional transformation of a sample mean. Its efficiency is compared with minimum variance unbiased estimates and then with the Cramér–Rao bound. We give conditions for a “small-sample effect” to occur, which means the advantage of pseudo-estimates according to mean-square criterion in the case of a small sample.