Draft:Iman-Conover method

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Instructions · What links here · Iman-Conover method (talk: + · bio) · (log) · Copyvios report · reFill · Citation Bot · (Search: Google, Wikipedia) · Submitted 24 hours ago by Thorpn86 (talk: D · +) · Last edited 4 hours ago by Citation bot

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 $\mathbf {X}$ be a data matrix and let $\mathbf {C}$ be a target rank-correlation matrix. the IC method rearranges the rows of $\mathbf {X}$ to form a new data matrix $\mathbf {W}$ with rank correlation close to $\mathbf {C}$ .

The method works as follows:

Create normal scores, $\mathbf {S}$ from $\mathbf {X}$
Uncorrelate the scores, define these as $\mathbf {Z}$
Transform $\mathbf {Z}$ to match the correlation matrix $\mathbf {C}$ , for example by the Cholesky decomposition, define these as $\mathbf {Y}$
Reorder the elements of $\mathbf {X}$ to match the ordering from $\mathbf {Y}$

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.

[IC-1] 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.

[IC2-2] 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.

[1]

[2]