taperingEst {cvCovEst} | R Documentation |

## Tapering Estimator

### Description

`taperingEst()`

estimates the covariance matrix of a
`data.frame`

-like object with ordered variables by gradually shrinking
the bands of the sample covariance matrix towards zero. The estimator is
defined as the Hadamard product of the sample covariance matrix and a
weight matrix. The amount of shrinkage is dictated by the weight matrix
and is specified by a hyperparameter `k`

. This estimator is attributed
to Cai et al. (2010).

The weight matrix is a Toeplitz matrix with entries defined as follows. Let
i and j index the rows and columns of the weight matrix, respectively. If
`abs(i - j) <= k / 2`

, then entry {i, j} in the weight matrix is
equal to 1. If `k / 2 < abs(i - j) < k`

, then entry {i, j} is equal
to `2 - 2 * abs(i - j) / k`

. Otherwise, entry {i, j} is equal to 0.

### Usage

```
taperingEst(dat, k)
```

### Arguments

`dat` |
A numeric |

`k` |
A non-negative, even |

### Value

A `matrix`

corresponding to the estimate of the covariance
matrix.

### References

Cai TT, Zhang C, Zhou HH (2010).
“Optimal rates of convergence for covariance matrix estimation.”
*Ann. Statist.*, **38**(4), 2118–2144.
doi:10.1214/09-AOS752.

### Examples

```
taperingEst(dat = mtcars, k = 0.1)
```

*cvCovEst*version 1.2.2 Index]