Procedural invariance. Consider a sample of 512 observations generated according to the model in the previous exercise. The estimation procedure is invariant if \(\hat{\beta}(Y)=\hat{\beta}\left(Y^{\tau}\right)\) and \(\hat{\sigma}(Y)=\hat{\sigma}\left(Y^{\tau}\right)\) for every baseline permutation. Is it necessarily the case that distributional invariance implies procedural invariance? Explain why least-squares and maximum-likelihood are invariant procedures.