A NEW HIGHER ORDER APPROXIMATION TO A PERCENTAGE POINT OF THE DISTRIBUTION OF THE SAMPLE CORRELATION COEFFICIENT

Abstract

A new higher order approximation formula for a percentage point of the distribution of the sample correlation coefficient is given up to the order O(n^-1), using the Cornish-Fisher expansion for the statistic based on a linear combination of a normal random variable and chi-random variables. The numerical comparison of the formula with others shows that it dominates the others and gives almost precise values in various cases even for the size n=10 of sample.