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.

翻译：本文针对Cox和Reid于1987年在其开创性论文中提出的统计推断中参数正交性问题进行了探讨。我们将正交性条件扩展至含多个感兴趣参数的情形，并证明在某些普遍重要的分布中，正交性在全局层面存在，尽管他们先前对此表达了悲观看法。以位置-尺度$t$分布为例的数值结果表明，由于正交性的存在，估计精度显著提升，计算时间大幅节省。进一步，我们证明局部参数正交性可催生高效的计算算法，并以多元自回归建模中著名的Whittle算法为例进行展示。