asymptotic variance of correlation coefficient?

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1 total messages Started by Hidetoshi SHIMODAIRA Mon, 14 Sep 1992 11:37

#332

Author: Hidetoshi SHIMODAIRA
Date: Mon, 14 Sep 1992 11:37

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Dear statisticians:

    I am a graduate student and reading RAO's text book, Linear
Statistical Inference and Its Applications. I have a little question
as follows.

    In the page 362 of the book, he says: The asymptotic variance of
the product moment correlation coefficient $r$ is $(1-\rho^2)^2/n$.
He uses this result to derive the Tanh^{-1} transformation of the
correlation coefficient.

    But I cannot understand why the asymptotic variance of r is
(1-rho^2)^2/n.  If someone know the proof or any pointers, please let
me know these.

Thank you,


 //\\\
  @ @     Hidetoshi SHIMODAIRA    <shimo@bcl.t.u-tokyo.ac.jp>
   O      Dept. of Math. Eng. & Info. Physics, Univ. of Tokyo

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