ON ONE TERM EDGEWORTH CORRECTION BY EFRON'S BOOTSTRAP

Efron (1979) introduced a resampling procedure called the 'bootstrap* for estimating the sampling distribution of a statistical function T(X, F), where X = {Xv X2, ..., Xn} is a random sample from an unknown popula tion F on Rk. Efron's bootstrap consists of approximating the distribution of T(X9 F) by that of T(Y, Fn) where Y = {Yv Y2, ..., Yn] is a random sample from the empirical d.f. Fn of X. The bootstrap procedure can be generalized by using a general estimate 0n of F based on X9 at the place of Fn. For further details on bootstrap and its applications to a number of statistical problems see Efron (1979, 1981). See Bickel and Freedman (1980) for some central limit theorems on the bootstrap.