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` in the null-distribution of the correlation coefficient (i.e. assuming that rho=0).

According to Fisher's rule `kappa = round(1/var(z) + 2)` the degree of freedom can be estimated from the variance of the z-transformed sample correlations.

Maximum-likelihood estimates of the degree of freedom is obtained on the basis of the null distribution of the sample correlation coefficient (i.e. assuming rho = 0) using `method="likelihood"`. 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".

The degree of freedom `kappa` depends both on the sample size N and the number G of investigated variables, i.e. whether simple or partial correlation coefficients are being considered. For G=2 (simple correlation coefficient) the degree of freedom equals kappa = N-1, whereas for arbitrary G (with G-2 variables eliminated in the partial correlation coefficient) kappa = N-G+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.

### 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

### Value

The estimated degree of freedom kappa.

### Author(s)

Juliane Schaefer (http://www.stat.uni-muenchen.de/~schaefer/) and Korbinian Strimmer (http://www.stat.uni-muenchen.de/~strimmer/).

`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 2.3 Index]