CovTest2.2013Cai {CovTools} | R Documentation |

## Two-Sample Covariance Test by Cai and Ma (2013)

### Description

Given two sets of data, it performs 2-sample test for equality of covariance matrices where the null hypothesis is

`H_0 : \Sigma_1 = \Sigma_2`

where `\Sigma_1`

and `\Sigma_2`

represent true (unknown) covariance
for each dataset based on a procedure proposed by Cai and Ma (2013).
If `statistic`

`>`

`threshold`

, it rejects null hypothesis.

### Usage

```
CovTest2.2013Cai(X, Y, alpha = 0.05)
```

### Arguments

`X` |
an |

`Y` |
an |

`alpha` |
level of significance. |

### Value

a named list containing

- statistic
a test statistic value.

- threshold
rejection criterion to be compared against test statistic.

- reject
a logical;

`TRUE`

to reject null hypothesis,`FALSE`

otherwise.

### References

Cai TT, Ma Z (2013).
“Optimal hypothesis testing for high dimensional covariance matrices.”
*Bernoulli*, **19**(5B), 2359–2388.
ISSN 1350-7265.

### Examples

```
## generate 2 datasets from multivariate normal with identical covariance.
pdim = 5
data1 = matrix(rnorm(100*pdim), ncol=pdim)
data2 = matrix(rnorm(150*pdim), ncol=pdim)
## run test
CovTest2.2013Cai(data1, data2)
```

*CovTools*version 0.5.4 Index]