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Regular version of the site

Book chapter

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

P. 239-260.
Christoph G., Fujikoshi Y., Ulyanov V. V.

In 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 different orders with respect to n  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.

In book

Edited by: A. N. Shiryaev, S. Varadhan, E. L. Presman. Vol. 33: Prokhorov and Contemporary Probability Theory, In Honor of Yuri V. Prokhorov, Series: Springer Proceedings in Mathematics & Statistics. Heidelberg: Springer, 2013.