DiagTest1.2011Cai {CovTools} | R Documentation |

## One-Sample Diagonality Test by Cai and Jiang (2011)

### Description

Given data, it performs 1-sample test for diagonal entries of a Covariance matrix where the null hypothesis is

`H_0 : \sigma_{ij} = 0~\mathrm{for any}~i \neq j`

and alternative hypothesis is `H_1 : ~\mathrm{not}~H_0`

with `\Sigma_n = (\sigma_{ij})`

based on a procedure proposed by Cai and Jiang (2011).

### Usage

```
DiagTest1.2011Cai(data, alpha = 0.05)
```

### Arguments

`data` |
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, Jiang T (2011).
“Limiting laws of coherence of random matrices with applications to testing covariance structure and construction of compressed sensing matrices.”
*The Annals of Statistics*, **39**(3), 1496–1525.
ISSN 0090-5364.

### Examples

```
## Not run:
## generate data from multivariate normal with trivial covariance.
pdim = 5
data = matrix(rnorm(100*pdim), ncol=pdim)
## run test with different alpha values
DiagTest1.2011Cai(data, alpha=0.01)
DiagTest1.2011Cai(data, alpha=0.05)
DiagTest1.2011Cai(data, alpha=0.10)
## End(Not run)
```

*CovTools*version 0.5.4 Index]