# The Generalized Fisher Transformation: Finite-Sample Properties and Inference

arXiv: https://arxiv.org/abs/2606.13864 · HTML: https://mlsanity.com/paper/2606.13864/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2026.

## Built on by (most cited first, 1 of 1)

- [CorrFlow: Exact and Permutation-Equivariant Flow Matching on the Correlation Elliptope](https://mlsanity.com/paper/2610.13606/) (2026)

## Abstract (arXiv)

We study the finite-sample behavior of the Generalized Fisher Transformation (GFT), the parametrization of a correlation matrix C by γ(C)=operatornamevecllog C. The GFT coordinates extend Fisher's transformation to dimension n>2: for elliptical data their finite-sample distributions are close to Gaussian. More strikingly, the coordinates are nearly uncorrelated and their covariance is largely invariant to C. This approximate orthogonality and invariance make GFT-based inference far better behaved in finite samples than inference based on sample correlations or element-wise Fisher transformed correlations, yielding estimation errors that are approximately Gaussian, weakly dependent, and nearly pivotal.