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Smooth estimation of mean and dispersion function in extended generalized additive models with application to Italian induced abortion data

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  • I. Gijbels
  • I. Prosdocimi

Abstract

We analyse data on abortion rate (AR) in Italy with a particular focus on different behaviours in different regions in Italy. The aim is to try to reveal the relationship between the AR and several covariates that describe in some way the modernity of the region and the condition of the women there. The data are mostly underdispersed and the degree of underdispersion also varies with the covariates. To analyse these data, recent techniques for flexible modelling of a mean and dispersion function in a double exponential family framework are further developed now in a generalized additive model context for dealing with the multivariate set-up. The appealing unified framework and approach even allow to semi-parametric modelling of the covariates without any additional efforts. The methodology is illustrated on ozone-level data and leads to interesting findings in the Italian abortion data.

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  • I. Gijbels & I. Prosdocimi, 2011. "Smooth estimation of mean and dispersion function in extended generalized additive models with application to Italian induced abortion data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(11), pages 2391-2411, December.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:11:p:2391-2411
    DOI: 10.1080/02664763.2010.550039
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    1. Marx, Brian D. & Eilers, Paul H. C., 1998. "Direct generalized additive modeling with penalized likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 28(2), pages 193-209, August.
    2. David Nott, 2006. "Semiparametric estimation of mean and variance functions for non-Gaussian data," Computational Statistics, Springer, vol. 21(3), pages 603-620, December.
    3. Yuan, Ming & Wahba, Grace, 2004. "Doubly penalized likelihood estimator in heteroscedastic regression," Statistics & Probability Letters, Elsevier, vol. 69(1), pages 11-20, August.
    4. I. Gijbels & I. Prosdocimi & G. Claeskens, 2010. "Nonparametric estimation of mean and dispersion functions in extended generalized linear models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 580-608, November.
    5. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, October.
    6. Youngjo Lee & John A. Nelder, 2006. "Double hierarchical generalized linear models (with discussion)," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(2), pages 139-185, April.
    7. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, October.
    8. Hinde, John & Demetrio, Clarice G. B., 1998. "Overdispersion: Models and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 27(2), pages 151-170, April.
    9. Simon N. Wood, 2008. "Fast stable direct fitting and smoothness selection for generalized additive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(3), pages 495-518, July.
    10. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
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    Cited by:

    1. Christophe Croux & Irène Gijbels & Ilaria Prosdocimi, 2012. "Robust Estimation of Mean and Dispersion Functions in Extended Generalized Additive Models," Biometrics, The International Biometric Society, vol. 68(1), pages 31-44, March.
    2. María Alonso‐Pena & Irène Gijbels & Rosa M. Crujeiras, 2023. "Flexible joint modeling of mean and dispersion for the directional tuning of neuronal spike counts," Biometrics, The International Biometric Society, vol. 79(4), pages 3431-3444, December.

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