C. D. Lai, J. C. W. Rayner, T. P. Hutchinson, "Robustness of the sample correlation - the bivariate lognormal case", Advances in Decision Sciences, vol. 3, Article ID 472545, 13 pages, 1999. https://doi.org/10.1155/S1173912699000012
Robustness of the sample correlation - the bivariate lognormal case
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.
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