Accurate Approximation of Correlation Coefficients by Short Edgeworth-Chebyshev Expansion and Its Statistical Applications

Abstract

AbstractIn Christoph, Prokhorov and Ulyanov (Theory Probab Appl 40(2):250–260, 1996) we studied properties of high-dimensional Gaussian random vectors. Yuri Vasil’evich Prokhorov initiated these investigations. In the present paper we continue these investigations. Computable error bounds of order O(n − 3) or O(n − 2) for the approximations of sample correlation coefficients and the angle between high-dimensional Gaussian vectors by the standard normal law are obtained. We give some numerical results as well. Moreover, different types of Bartlett corrections are suggested.KeywordsHigh-dimensional Gaussian random vectorsSample correlation coefficientShort Edgeworth-Chebyshev expansionsComputable error boundBartlett correctionFisher transform