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

C. Croux, I. Gijbels, I. Prosdocimi

Research output: Working paperDiscussion paperOther research output

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Abstract

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.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages21
Volume2010-104
Publication statusPublished - 2010

Publication series

NameCentER Discussion Paper
Volume2010-104

Fingerprint

Generalized Additive Models
Robust Estimation
Quasi-likelihood
Estimate
Robust Estimate
Maximum Likelihood Method
Generalized Linear Model
Outlier
Covariates
Simulation Study

Keywords

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

Cite this

Croux, C., Gijbels, I., & Prosdocimi, I. (2010). Robust Estimation of Mean and Dispersion Functions in Extended Generalized Additive Models. (CentER Discussion Paper; Vol. 2010-104). Tilburg: Econometrics.
Croux, C. ; Gijbels, I. ; Prosdocimi, I. / Robust Estimation of Mean and Dispersion Functions in Extended Generalized Additive Models. Tilburg : Econometrics, 2010. (CentER Discussion Paper).
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Croux, C, Gijbels, I & Prosdocimi, I 2010 'Robust Estimation of Mean and Dispersion Functions in Extended Generalized Additive Models' CentER Discussion Paper, vol. 2010-104, Econometrics, Tilburg.

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

Tilburg : Econometrics, 2010. (CentER Discussion Paper; Vol. 2010-104).

Research output: Working paperDiscussion paperOther 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 -

Croux C, Gijbels I, Prosdocimi I. Robust Estimation of Mean and Dispersion Functions in Extended Generalized Additive Models. Tilburg: Econometrics. 2010. (CentER Discussion Paper).