An asymptotic expansion of bias in a non-linear function of a set of unbiased characteristics from a finite sample

Abstract

Very often one has to make an estimate of some function f (m) of a certain characteristic m belonging to a certain distribution. However, m is often unknown and then it may be necessary, somehow, to estimate m with the corresponding unbiased characteristic x from a sample consisting of n individuals which may be one- or multidimensional. If f (x) is a linear function it is evident that .