Let R' = R + D be the estimated correlation matrix, where R is the original correlation matrix and D is the matrix that models the estimation error. My question is the existence of models for this matrix D.
Dear Jordi,
In the area of modelization all could be possible, infinite models could be used theoretically for your fuzzy purpose. But, in practice, when there is a clear objective and certain conditions of work, it is possible to see ways of optimization.
I think that subjective modelization does not give more adventages than the use of the objective and defined conditions of work.
Jordi,
If your correlation estimate comes from multivariate normal(Gaussian) distribution, The estimated correlation matrix (your R'), it will have the distribution of Wishart(R,df), where df is the number of degrees of freedom (usually, n - p +1, n is the number of samples you use and p is the size of R) Then, the expected value of the estimator for R' (the theoretical average of many estimated values of R') is R/(n-1) .
Hope this can help as well.
Reference: Anderson T.W., An introduction to Multivariate Analysis, Third edition - Chapter 7
and correction : R' distributed Wishart(R/(N-1),N-1),
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