Ilya Archakov, Peter Reinhard Hansen
arXiv 11 Jun 2026 · Econometrics
arXiv:2606.13864 · PDF · DOI · OpenAlex · Extracted main text
We study the finite-sample behavior of the Generalized Fisher Transformation (GFT), the parametrization of a correlation matrix $C$ by $γ(C)=\operatorname{vecl}\log C$. 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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Archakov, I. and P. R. Hansen (2021) A new parametrization of correlation matrices self | 0.928 | 5 | 3 | 80% |
| 2 | McCracken, M. W. and S. Ng (2016) FRED-MD: A monthly database for macroeconomic research | 0.737 | 3 | 3 | 67% |
| 3 | Fisher, R. A (1921) On the 'probable error' of a coefficient of correlation deduced from a small sample | 0.511 | 2 | 1 | 100% |
| 4 | Andersen, T. G., T. Bollerslev, F. X. Diebold, and H. Ebens (2001) The distribution of realized stock return volatility | 0.405 | 1 | 1 | 100% |
| 5 | Andersen, T. G., T. Bollerslev, F. X. Diebold, and P. Labys (2001) The distribution of realized exchange rate volatility | 0.405 | 1 | 1 | 100% |
| 6 | Archakov, I., P. R. Hansen, and Y. Luo (2024) A new method for generating random correlation matrices self | 0.405 | 1 | 1 | 100% |
| 7 | Fisher, R. A (1915) Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population | 0.405 | 1 | 1 | 100% |
| 8 | Hansen, P. R. and Y. Luo (2023) Robust estimation of realized correlation: New insight about intraday fluctuations in market betas self | 0.405 | 1 | 1 | 100% |
| 9 | Hotelling, H (1953) New light on the correlation coefficient and its transforms | 0.405 | 1 | 1 | 100% |
| 10 | Browne, M. W. and A. Shapiro (1986) The asymptotic covariance matrix of sample correlation coefficients under general conditions | 0.000 | 2 | 2 | 0% |
Showing the top 10 of 15 scored citations.