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

P. 239–260.

Christoph G., Fujikoshi Y., Ульянов В. В.

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.

Ключевые слова: High-dimensional Gaussian random vectors, Sample correlation coefficient, Short Edgeworth-Chebyshev expansions, Computable error bound, Bartlett correction, Fisher transform

В книге

Prokhorov and Contemporary Probability Theory

Vol. 33: Prokhorov and Contemporary Probability Theory, In Honor of Yuri V. Prokhorov, Series: Springer Proceedings in Mathematics & Statistics. , Heidelberg: Springer, 2013.