### Abstract

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

Place of Publication | Tilburg |

Publisher | Econometrics |

Number of pages | 21 |

Volume | 2010-104 |

Publication status | Published - 2010 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2010-104 |

### Fingerprint

### Keywords

- dispersion
- generalized additive modelling
- mean regression function
- quasilikelihood
- M-estimation
- P-splines
- robust estimation

### Cite this

*Robust Estimation of Mean and Dispersion Functions in Extended Generalized Additive Models*. (CentER Discussion Paper; Vol. 2010-104). Tilburg: Econometrics.

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**Robust Estimation of Mean and Dispersion Functions in Extended Generalized Additive Models.** / Croux, C.; Gijbels, I.; Prosdocimi, I.

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

TY - UNPB

T1 - Robust Estimation of Mean and Dispersion Functions in Extended Generalized Additive Models

AU - Croux, C.

AU - Gijbels, I.

AU - Prosdocimi, I.

N1 - Pagination: 21

PY - 2010

Y1 - 2010

N2 - Generalized Linear Models are a widely used method to obtain parametric es- timates for the mean function. They have been further extended to allow the re- lationship between the mean function and the covariates to be more flexible via Generalized Additive Models. However the fixed variance structure can in many cases be too restrictive. The Extended Quasi-Likelihood (EQL) framework allows for estimation of both the mean and the dispersion/variance as functions of covari- ates. As for other maximum likelihood methods though, EQL estimates are not resistant to outliers: we need methods to obtain robust estimates for both the mean and the dispersion function. In this paper we obtain functional estimates for the mean and the dispersion that are both robust and smooth. The performance of the proposed method is illustrated via a simulation study and some real data examples.

AB - Generalized Linear Models are a widely used method to obtain parametric es- timates for the mean function. They have been further extended to allow the re- lationship between the mean function and the covariates to be more flexible via Generalized Additive Models. However the fixed variance structure can in many cases be too restrictive. The Extended Quasi-Likelihood (EQL) framework allows for estimation of both the mean and the dispersion/variance as functions of covari- ates. As for other maximum likelihood methods though, EQL estimates are not resistant to outliers: we need methods to obtain robust estimates for both the mean and the dispersion function. In this paper we obtain functional estimates for the mean and the dispersion that are both robust and smooth. The performance of the proposed method is illustrated via a simulation study and some real data examples.

KW - dispersion

KW - generalized additive modelling

KW - mean regression function

KW - quasilikelihood

KW - M-estimation

KW - P-splines

KW - robust estimation

M3 - Discussion paper

VL - 2010-104

T3 - CentER Discussion Paper

BT - Robust Estimation of Mean and Dispersion Functions in Extended Generalized Additive Models

PB - Econometrics

CY - Tilburg

ER -