Asymptotics for linear approximations of smooth functions of means

Abstract

A higher-order version of the linear approximation of smooth functions of means proposed in Pallini (2002) is defined and studied. This version is shown to improve over the error of order Op(n -2) in probability, as the sample size n diverges, yielding a smaller error of order Op(n -3), as n diverges. Both linear approximations are shown to have a normal distribution, as diverges. Empirical results of a simulation study on the ratio of means example are presented.