A note on parameter orthogonality for multi-parameter distributions

TL;DR

This paper explores parameter orthogonality in multi-parameter distributions, demonstrating its existence and benefits for estimation accuracy and computational efficiency in statistical inference.

Contribution

It extends the concept of parameter orthogonality to multiple parameters and shows its practical advantages in estimation and computation.

Findings

Existence of global parameter orthogonality in important distributions

Substantial gains in estimation accuracy with orthogonality

Computational savings using orthogonality in algorithms

Abstract

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.