How to transform correlated random variables into uncorrelated ones Original Research Article

For an arbitrary random vector View the MathML source, we can always construct uncorrelated random variables Y1, Y2,…, Yn and (R → R) functions f1, f2,…, fn, such that (X1, X2,…, Xn) = (f1(Y1), f2(Y2),…, fn(Yn)). Although the fs cannot always be one-to-one, in many important cases, the fs are not only one-to-one but also piecewise linear, e.g., if X is normally distributed. (This way, in many statistical models, the nuisance parameters can easily be transformed, such that their MLEs become uncorrelated with other parameters.)