cor0.estimate.kappa {GeneTS}R Documentation

Estimating the Degree of Freedom of the Null Distribution of the Correlation Coefficient

Description

cor0.estimate.kappa estimates the degree of freedom kappa of the null-distribution of the correlation coefficient r using a variety of methods.

If method="fisher" is selected then kappa is estimated according to Fisher's rule, i.e. kappa = round(1/var(z.transform(r)) + 2).

If method="likelihood" is selected then the ML estimate is computed by optimizing kappa in the null distribution of the sample correlation coefficient. This results almost always in the same estimate of kappa as with the simple Fisher's rule.

If method="robust" then the variance employed in Fisher's rule is estimated using the Huber M-estimate of the scale. This is useful if the null-distribution is slightly "contaminated".

Usage

cor0.estimate.kappa(r, method=c("fisher", "likelihood", "robust"), MAXKAPPA=5000, w=1.0)

Arguments

r vector of sample correlations (assumed true value of rho=0)
method use Fisher's rule (fisher), optimize likelihood function of null distribution (likelihood), or use Fisher's rule with robust estimate of variance (robust),
MAXKAPPA upper bound for the estimated kappa (default: MAXKAPPA=5000); only for likelihood estimate
w winsorize at `w' standard deviations; only for robust estimate

Details

The degree of freedom kappa of the distribution of the sample correlation coefficient depends both on the sample size n and the number p of investigated variables. For rho=0 the degree of freedom kappa equals the inverse of the variance of r.

For p=2 (simple correlation coefficient) the degree of freedom equals kappa = n-1, whereas for arbitrary p (with p-2 variables eliminated in the partial correlation coefficient) kappa = n-p+1 (see also dcor0 and kappa2n).

If the empirical sampling distribution is a mixture distribution then use of cor0.estimate.kappa may not be appropriate; instead cor.fit.mixture may be used.

Value

The estimated degree of freedom kappa.

Author(s)

Juliane Schaefer (http://www.statistik.lmu.de/~schaefer/) and Korbinian Strimmer (http://www.statistik.lmu.de/~strimmer/).

See Also

dcor0, z.transform, hubers, kappa2n, cor.fit.mixture.

Examples

# load GeneTS library
library("GeneTS")

# distribution of r for kappa=7
x <- seq(-1,1,0.01)
y <- dcor0(x, kappa=7)

# simulated data
r <- rcor0(1000, kappa=7)
hist(r, freq=FALSE, 
  xlim=c(-1,1), ylim=c(0,5))
lines(x,y,type="l")

# estimate kappa
cor0.estimate.kappa(r)

[Package GeneTS version 2.8.0 Index]