The probability integral of the sample correlation coefficient

1992 ◽  
Vol 1 (2) ◽  
pp. 289-294 ◽  
Author(s):  
Luigi Greco
Keyword(s):  
Correlation Coefficient ◽  
Sample Correlation ◽  
Probability Integral

Using Incidence Sampling to Estimate Covariances

1979 ◽  
Vol 4 (1) ◽  
pp. 41-58 ◽  
Author(s):  
Thomas R. Knapp
Keyword(s):  
Missing Data ◽  
Correlation Coefficient ◽  
Sample Covariance ◽  
Sample Correlation

This paper is an attempt to illustrate the generality of incidence sampling for estimating a parameter whose estimator preserves the unbiasedness of generalized symmetric means, a property which the sample covariance possesses but which the sample correlation coefficient does not. The problem of missing data is also addressed.

On the Distribution of the Sample Correlation Coefficient

1992 ◽  
pp. 466-469
Author(s):  
N. N. Mikhail ◽  
F. A. Chimenti ◽  
J. D. Kidder
Keyword(s):  
Correlation Coefficient ◽  
Sample Correlation

LSTUR regression theory and the instability of the sample correlation coefficient between financial return indices

2020 ◽  
Author(s):  
Tim Ginker ◽  
Offer Lieberman
Keyword(s):  
Correlation Coefficient ◽  
Unit Root ◽  
Asymptotic Theory ◽  
Financial Return ◽  
Spurious Regression ◽  
Root Model ◽  
Sampling Window ◽  
Sample Correlation ◽  
Underlying Processes ◽  
Regression Theory

Summary It is well known that the sample correlation coefficient between many financial return indices exhibits substantial variation on any reasonable sampling window. This stylised fact contradicts a unit root model for the underlying processes in levels, as the statistic converges in probability to a constant under this modeling scheme. In this paper, we establish asymptotic theory for regression in local stochastic unit root (LSTUR) variables. An empirical application reveals that the new theory explains very well the instability, in both sign and scale, of the sample correlation coefficient between gold, oil, and stock return price indices. In addition, we establish spurious regression theory for LSTUR variables, which generalises the results known hitherto, as well as a theory for balanced regression in this setting.

A Monte Carlo Investigation of the Fisher Z Transformation for Normal and Nonnormal Distributions

2000 ◽  
Vol 87 (3_suppl) ◽  
pp. 1101-1114 ◽  
Author(s):  
Kenneth J. Berry ◽  
Paul W. Mielke
Keyword(s):  
Monte Carlo ◽  
Correlation Coefficient ◽  
Bivariate Normal Distribution ◽  
Small Samples ◽  
Bivariate Distributions ◽  
Nonnormal Distributions ◽  
Monte Carlo Investigation ◽  
Sample Correlation ◽  
Heavy Tailed ◽  
Z Transformation

The Fisher transformation of the sample correlation coefficient r (1915, 1921) and two related techniques by Gayen (1951) and Jeyaratnam (1992) are examined for robustness to nonnormality. Monte Carlo analyses compare combinations of sample sizes and population parameters for seven bivariate distributions. The Fisher, Gayen, and Jeyaratnam approaches are shown to provide useful results for a bivariate normal distribution with any population correlation coefficient ρ and for nonnormal bivariate distributions when ρ = 0. In contrast, the techniques are virtually useless for nonnormal bivariate distributions when ρ#0.0. Surprisingly, small samples are found to provide better estimates than large samples for skewed and symmetric heavy-tailed bivariate distributions.

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