Draft:Iman-Conover method
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The Iman-Conover (IC) method or transformation is a statistical method for generating a sample with a specified rank-correlation[1].
Description of full method
[edit]The IC method takes as input a set of data and a target correlation matrix. The method works by rearranging the data to achieve a rank correlation close to the target correlation matrix.
Let be a data matrix and let be a target rank-correlation matrix. the IC method rearranges the rows of to form a new data matrix with rank correlation close to .
The method works as follows:
- Create normal scores, from
- Uncorrelate the scores, define these as
- Transform to match the correlation matrix , for example by the Cholesky decomposition, define these as
- Reorder the elements of to match the ordering from
Strong uniform consistency of the estimated sum distribution function is prooved[2].
A simpler version involves simulating directly from a specified copula and using the resulting output to reorder as in step 4 above.
References
[edit]- ^ Iman, Ronald L.; Conover, W. J. (Jan 1981). "A distribution-free approach to inducing rank correlation among input variables". Communications in Statistics - Simulation and Computation. 11 (3). Taylor & Francis: 311–334. doi:10.1080/03610918208812265.
- ^ Mainik, Georg (2015). "Risk aggregation with empirical margins: Latin hypercubes, empirical copulas, and convergence of sum distributions". Journal of Multivariate Analysis. 141. Elsevier: 197–216. doi:10.1016/j.jmva.2015.07.008.