robustPoetEst {cvCovEst} | R Documentation |

## Robust POET Estimator for Elliptical Distributions

### Description

`robustPoetEst()`

implements the robust version of
Principal Orthogonal complEment Thresholding (POET) estimator, a
nonparametric, unobserved-factor-based estimator of the covariance matrix
when the underlying distribution is elliptical
(Fan et al. 2018). The estimator is defined as the sum of the
sample covariance matrix's rank-`k`

approximation and its
post-thresholding principal orthogonal complement. The rank-`k`

approximation is constructed from the sample covariance matrix, its leading
eigenvalues, and its leading eigenvectors. The sample covariance matrix and
leading eigenvalues are initially estimated via an M-estimation procedure
and the marginal Kendall's tau estimator. The leading eigenvectors are
estimated using spatial Kendall's tau estimator. The hard thresholding
function is used to regularize the idiosyncratic errors' estimated
covariance matrix, though other regularization schemes could be used.

We do not recommend that this estimator be employed when the estimand is the correlation matrix. The diagonal entries of the resulting estimate are not guaranteed to be equal to one.

### Usage

```
robustPoetEst(dat, k, lambda, var_est = c("sample", "mad", "huber"))
```

### Arguments

`dat` |
A numeric |

`k` |
An |

`lambda` |
A non-negative |

`var_est` |
A |

### Value

A `matrix`

corresponding to the estimate of the covariance
matrix.

### References

Fan J, Liao Y, Mincheva M (2013).
“Large covariance estimation by thresholding principal orthogonal complements.”
*Journal of the Royal Statistical Society. Series B (Statistical Methodology)*, **75**(4), 603–680.
ISSN 13697412, 14679868, https://www.jstor.org/stable/24772450.

Fan J, Liu H, Wang W (2018).
“Large covariance estimation through elliptical factor models.”
*Ann. Statist.*, **46**(4), 1383–1414.
doi:10.1214/17-AOS1588.

### Examples

```
robustPoetEst(dat = mtcars, k = 2L, lambda = 0.1, var_est = "sample")
```

*cvCovEst*version 1.2.2 Index]