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.

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

The method works as follows:

1. Create normal scores, $𝐒$ from $𝐗$
2. Uncorrelate the scores, define these as $𝐙$
3. Transform $𝐙$ to match the correlation matrix $𝐂$, for example by the Cholesky decomposition, define these as $𝐘$
4. Reorder the elements of $𝐗$ to match the ordering from $𝐘$

Strong uniform consistency of the estimated sum distribution function is prooved.

A simpler version involves simulating directly from a specified copula and using the resulting output to reorder as in step 4 above.