A note on parameter orthogonality for multi-parameter distributions

This note addresses issues raised by Cox and Reid in their seminal paper in 1987 regarding parameter orthogonality in statistical inference. We extend the orthogonality condition to cases with multiple parameters of interest and demonstrate its existence at a global level for some generally important distributions, despite previously expressed pessimism by them. Numerical results with the location-scale $t$-distribution reveal substantial gains in estimation accuracy and savings in computation time, thanks to the existence. We next show that the local parameter orthogonality can lead to efficient computational algorithms with the celebrated Whittle algorithm for multivariate autoregressive modeling as a showcase.