Draft:Iman-Conover method
Description of Iman-Conover method for inducing rank correlation
 | This article, Draft:Iman-Conover method, has recently been created via the Articles for creation process. Please check to see if the reviewer has accidentally left this template after accepting the draft and take appropriate action as necessary.
Reviewer tools: Preload talk Inform author |
| This article, Draft:Iman-Conover method, has recently been created via the Articles for creation process. Please check to see if the reviewer has accidentally left this template after accepting the draft and take appropriate action as necessary.
Reviewer tools: Preload talk Inform author |
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
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
- ^ 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.