I am working on some simulations using the Iman-Conover method to sample correlated random variables so I can have a 'population' Spearman correlation parameter as opposed to a Pearson correlation (like in the case of the bivariate normal distribution). But I am encountering a problem that doesn't seem to be addressed in the literature.

From what I understood, if you sample data from a bivariate distribution using the Iman-Conover method with normal scores, this is analogously to sampling data from a bivariate Gaussian copula. Now, the Gaussian copula corresponds to the multivariate Gaussian distribution if the marginals are normally-distributed... which makes me think that if I sample data using the Iman-Conover method specifying normal marginals and normal scores I'm essentially sampling data from a bivariate normal distribution.

However, if I do this and calculate Mardia's Kurtosis on the data, it gives me a significant p-value saying the distribution is not bivariate normal. I've ran preliminary simulations and, indeed, Mardia's Kurtosis is significant in many cases.

I'm using the cornode() function from the mc2d package and when I looked at the code I can effectively see that this function uses normal scores.

I'm kind of stumped now... Has anyone ran into this problem? Most of the literature related to the Iman-Conover algorithm only talks about specifying the marginal distributions... very little info is out there explaining how the multivariate distribution looks like. Help? :)

  • $\begingroup$ The function cornnode has some error. Look at the bivariate plot where it can be seen. $\endgroup$ – user105145 Feb 14 '16 at 22:27

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