### Abstract

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

Place of Publication | Tilburg |

Publisher | Econometrics |

Number of pages | 25 |

Volume | 2008-40 |

Publication status | Published - 2008 |

### Publication series

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

Volume | 2008-40 |

### Fingerprint

### Keywords

- independence copula
- nonparametric maximum likelihood estimator
- score function
- semiparametric efficiency
- tangent space

### Cite this

*Improving Upon the Marginal Empirical Distribution Functions when the Copula is Known*. (CentER Discussion Paper; Vol. 2008-40). Tilburg: Econometrics.

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**Improving Upon the Marginal Empirical Distribution Functions when the Copula is Known.** / Segers, J.J.J.; van den Akker, R.; Werker, B.J.M.

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

TY - UNPB

T1 - Improving Upon the Marginal Empirical Distribution Functions when the Copula is Known

AU - Segers, J.J.J.

AU - van den Akker, R.

AU - Werker, B.J.M.

N1 - Pagination: 25

PY - 2008

Y1 - 2008

N2 - At the heart of the copula methodology in statistics is the idea of separating marginal distributions from the dependence structure. However, as shown in this paper, this separation is not to be taken for granted: in the model where the copula is known and the marginal distributions are completely unknown, the empirical distribution functions are semiparametrically efficient if and only if the copula is the independence copula. Incorporating the knowledge of the copula into a nonparametric likelihood yields an estimation procedure which by simulations is shown to outperform the empirical distribution functions, the amount of improvement depending on the copula. Although the known-copula model is arguably artificial, it provides an instructive stepping stone to the more general model of a parametrically specified copula and arbitrary margins.

AB - At the heart of the copula methodology in statistics is the idea of separating marginal distributions from the dependence structure. However, as shown in this paper, this separation is not to be taken for granted: in the model where the copula is known and the marginal distributions are completely unknown, the empirical distribution functions are semiparametrically efficient if and only if the copula is the independence copula. Incorporating the knowledge of the copula into a nonparametric likelihood yields an estimation procedure which by simulations is shown to outperform the empirical distribution functions, the amount of improvement depending on the copula. Although the known-copula model is arguably artificial, it provides an instructive stepping stone to the more general model of a parametrically specified copula and arbitrary margins.

KW - independence copula

KW - nonparametric maximum likelihood estimator

KW - score function

KW - semiparametric efficiency

KW - tangent space

M3 - Discussion paper

VL - 2008-40

T3 - CentER Discussion Paper

BT - Improving Upon the Marginal Empirical Distribution Functions when the Copula is Known

PB - Econometrics

CY - Tilburg

ER -