Exact mean and covariance formulas after diagonal transformations of a multivariate normal

Rebecca Morrison, Estelle Basor

Consider $\mathbf{X}\sim \mathcal{N}(0,\hat{\mathbf{I}}\pounds )$ and $\mathbf{Y}=(f_1(X_1),f_2(X_2),\dots ,f_d(X_d))$. We call this a diagonal transformation of a mul…