### Abstract

Original language | English |
---|---|

Place of Publication | Tilburg |

Publisher | Econometrics |

Number of pages | 24 |

Volume | 2014-035 |

Publication status | Published - 29 May 2014 |

### Publication series

Name | CentER Discussion Paper |
---|---|

Volume | 2014-035 |

### Fingerprint

### Keywords

- Extreme value statistics
- halfspace depth
- multivariate quantile
- outlier detection
- rare event
- tail dependence

### Cite this

*Estimation of Extreme Depth-Based Quantile Regions*. (CentER Discussion Paper; Vol. 2014-035). Tilburg: Econometrics.

}

**Estimation of Extreme Depth-Based Quantile Regions.** / He, Y.; Einmahl, J.H.J.

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - Estimation of Extreme Depth-Based Quantile Regions

AU - He, Y.

AU - Einmahl, J.H.J.

PY - 2014/5/29

Y1 - 2014/5/29

N2 - Consider the extreme quantile region, induced by the halfspace depth function HD, of the form Q = fx 2 Rd : HD(x; P) g, such that PQ = p for a given, very small p > 0. This region can hardly be estimated through a fully nonparametric procedure since the sample halfspace depth is 0 outside the convex hull of the data. Using Extreme Value Theory, we construct a natural, semiparametric estimator of this quantile region and prove a refined consistency result. A simulation study clearly demonstrates the good performance of our estimator. We use the procedure for risk management by applying it to stock market returns.

AB - Consider the extreme quantile region, induced by the halfspace depth function HD, of the form Q = fx 2 Rd : HD(x; P) g, such that PQ = p for a given, very small p > 0. This region can hardly be estimated through a fully nonparametric procedure since the sample halfspace depth is 0 outside the convex hull of the data. Using Extreme Value Theory, we construct a natural, semiparametric estimator of this quantile region and prove a refined consistency result. A simulation study clearly demonstrates the good performance of our estimator. We use the procedure for risk management by applying it to stock market returns.

KW - Extreme value statistics

KW - halfspace depth

KW - multivariate quantile

KW - outlier detection

KW - rare event

KW - tail dependence

M3 - Discussion paper

VL - 2014-035

T3 - CentER Discussion Paper

BT - Estimation of Extreme Depth-Based Quantile Regions

PB - Econometrics

CY - Tilburg

ER -