CovTest1.2013Cai {CovTools} | R Documentation |

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

### Description

Given data, it performs 1-sample test for Covariance where the null hypothesis is

`H_0 : \Sigma_n = \Sigma_0`

where `\Sigma_n`

is the covariance of data model and `\Sigma_0`

is a
hypothesized covariance based on a procedure proposed by Cai and Ma (2013).

### Usage

```
CovTest1.2013Cai(data, Sigma0 = diag(ncol(data)), alpha = 0.05)
```

### Arguments

`data` |
an |

`Sigma0` |
a |

`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

```
## Not run:
## generate data from multivariate normal with trivial covariance.
pdim = 5
data = matrix(rnorm(10*pdim), ncol=pdim)
## run the test
CovTest1.2013Cai(data)
## End(Not run)
```

[Package

*CovTools*version 0.5.4 Index]