Variance-stabilizing and Confidence-stabilizing Transformations for the Normal Correlation Coefficient with Known Variances

Fosdick and Raftery (2012) recently encountered the problem of inference for a bivariate normal correlation coefficient ρ with known variances. We derive a variance-stabilizing transformation y(ρ) analogous to Fisher's classical z-transformation for the unknown-variance case. Adjusting y for th...

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Bibliographic Details
Published in:Communications in statistics. Simulation and computation 2016-07, Vol.45 (6), p.1918-1935
Main Authors: Fosdick, Bailey K., Perlman, Michael D.
Format: Article
Language:English
Subjects:
Adjustment
Bivariate normal correlation
Computer simulation
Confidence intervals
Correlation coefficients
Estimates
Hypothesis tests
Intervals
Primary 62F12
Samples
Secondary 62F25
Small mammals
Statistical analysis
Transformations
Variance-stabilizing transformations
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Summary:Fosdick and Raftery (2012) recently encountered the problem of inference for a bivariate normal correlation coefficient ρ with known variances. We derive a variance-stabilizing transformation y(ρ) analogous to Fisher's classical z-transformation for the unknown-variance case. Adjusting y for the sample size n produces an improved "confidence-stabilizing" transformation y n (ρ) that provides more accurate interval estimates for ρ than the known-variance MLE. Interestingly, the z transformation applied to the unknown-but-equal-variance MLE performs well in the known-variance case for smaller values of |ρ|. Both methods are useful for comparing two or more correlation coefficients in the known-variance case.
ISSN:0361-0918
1532-4141
DOI:10.1080/03610918.2014.882948