Journal of Applied Mathematics and Decision Sciences
Volume 3 (1999), Issue 1, Pages 7-19
Robustness of the sample correlation - the bivariate lognormal case
1Statistics, IIST, Massey University, New Zealand
2School of Mathematics and Applied Statistics, University of Wollongong, Australia
3School of Behavioural Sciences, Macquarie University, Australia
Copyright © 1999 C. D. Lai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The sample correlation coefficient is almost universally used to estimate the
population correlation coefficient . If the pair
has a bivariate normal distribution, this
would not cause any trouble. However, if the marginals are nonnormal, particularly if they
have high skewness and kurtosis, the estimated value from a sample may be quite different from
the population correlation coefficient .
The bivariate lognormal is chosen as our case study for this robustness study. Two approaches
are used: (i) by simulation and (ii) numerical computations.
Our simulation analysis indicates that for the bivariate lognormal, the bias in estimating can
be very large if , and it can be substantially reduced only after a large number (three to four
million) of observations. This phenomenon, though unexpected at first, was found to be
consistent to our findings by our numerical analysis.