HIGHER ORDER ACCURATE CONFIDENCE INTERVALS FOR SMOOTH FUNCTIONS OF MEANS WITH APPLICATION TO THE CORRELATION COEFFICIENT

Higher order asymptotic expansions for studentized statistics under smooth function model are developed. The emphasis is on constructing higher order accurate confidence intervals, for parameters being smooth functions of means, based on the third order inverse Edgeworth expansions. The asymptotic results developed here are compared with similar results previously derived for the delete-one jackknife-t statistics. Extensive Monte Carlo studies are carried out in the case of estimating the correlation coefficient from bivariate normal populations. Comparisons are also made with the standard confidence intervals based on Fisher's normal approximation, which serves as a good bench mark in estimating the correlation coefficient.