Advances in Decision Sciences
Volume 3 (1999), Issue 1, Pages 7-19
doi:10.1155/S1173912699000012

Robustness of the sample correlation -- the bivariate lognormal case

C.D. Lai1 , J.C.W. Rayner2 and T.P. Hutchinson3

1Statistics, IIST, Massey University, New Zealand
 2School of Mathematics and Applied Statistics, University of Wollongong, Australia
 3School of Behavioural Sciences, Macquarie University, Australia

Abstract

The sample correlation coefficient R is almost universally used to estimate the population correlation coefficient ρ. If the pair (X,Y) 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 ρ.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 ρ can be very large if ρ≠0, 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.