Fuzzy sets theory has successfully accommodated the lack of clear-cut boundaries of poverty and i... more Fuzzy sets theory has successfully accommodated the lack of clear-cut boundaries of poverty and its gradual nature. On the other hand, uncertainties related to lack of knowledge and imprecision in poverty data need also to be accounted for. The accuracy of poverty analysis is highly subject to how well these features are adequately addressed. We argue that possibility theory is an appropriate framework to deal with incomplete knowledge in poverty. Indeed, considering "the possibility of poverty" instead of the "probability of poverty" allows us to achieve a more realistic handling of this phenomenon. Empirical possibility distributions of monetary poverty states are derived based on our previous works and alpha-cut analysis is used to explore their features. Also, collective possibilistic poverty measures for each state are computed along with an aggregate possibilistic poverty ratio. This possibilistic modeling is applied to the analysis of poverty in Tunisia in 2005 and 2010.
The excess of zeros is a not a rare feature in count data. Statisticians advocate the Poisson-typ... more The excess of zeros is a not a rare feature in count data. Statisticians advocate the Poisson-type hurdle model (among other techniques) as an interesting approach to handle this data peculiarity. However, the frequency of gross errors and the complexity intrinsic to some considered phenomena may render this classical model unreliable and too limiting. In this paper, we develop a robust version of the Poisson hurdle model by extending the robust procedure for GLM (Cantoni and Ronchetti, 2001) to the truncated Poisson regression model. The performance of the new robust approach is then investigated via a simulation study, a real data application and a sensitivity analysis. The results show the reliability of the new technique in the neighborhood of the truncated Poisson model. This robust modelling approach is therefore a valuable complement to the classical one, providing a tool for reliable statistical conclusions and to take more effective decisions.
Fuzzy sets theory has successfully accommodated the lack of clear-cut boundaries of poverty and i... more Fuzzy sets theory has successfully accommodated the lack of clear-cut boundaries of poverty and its gradual nature. On the other hand, uncertainties related to lack of knowledge and imprecision in poverty data need also to be accounted for. The accuracy of poverty analysis is highly subject to how well these features are adequately addressed. We argue that possibility theory is an appropriate framework to deal with incomplete knowledge in poverty. Indeed, considering "the possibility of poverty" instead of the "probability of poverty" allows us to achieve a more realistic handling of this phenomenon. Empirical possibility distributions of monetary poverty states are derived based on our previous works and alpha-cut analysis is used to explore their features. Also, collective possibilistic poverty measures for each state are computed along with an aggregate possibilistic poverty ratio. This possibilistic modeling is applied to the analysis of poverty in Tunisia in 2005 and 2010.
Fuzzy conceptualization of privation has been a step closer to more realistic handling of poverty... more Fuzzy conceptualization of privation has been a step closer to more realistic handling of poverty. However, fuzzy approaches to poverty are still grounded on parametric axioms. Moreover, construction of poverty lines within these approaches still relies on ad-hoc methods. In this paper, we advance instead a fuzzy procedure based on the non-parametric bootstrap method, allowing us to depict fuzzy unidimensional privation states with boundaries drawn spontaneously from data. Fuzzy nonparametric measures of privation within each state as well as a collective fuzzy non-parametric index of poverty are derived, along with their corresponding confidence intervals. The new approach is applied to the analysis of poverty in Tunisia in 2005.
Journal of Statistical Planning and Inference, 2011
The excess of zeros is a not a rare feature in count data. Statisticians advocate the Poisson-typ... more The excess of zeros is a not a rare feature in count data. Statisticians advocate the Poisson-type hurdle model (among other techniques) as an interesting approach to handle this data peculiarity. However, the frequency of gross errors and the complexity intrinsic to some considered phenomena may render this classical model unreliable and too limiting. In this paper, we develop a robust version of the Poisson hurdle model by extending the robust procedure for GLM (Cantoni and Ronchetti, 2001) to the truncated Poisson regression model. The performance of the new robust approach is then investigated via a simulation study, a real data application and a sensitivity analysis. The results show the reliability of the new technique in the neighborhood of the truncated Poisson model. This robust modelling approach is therefore a valuable complement to the classical one, providing a tool for reliable statistical conclusions and to take more effective decisions.
Fuzzy sets theory has successfully accommodated the lack of clear-cut boundaries of poverty and i... more Fuzzy sets theory has successfully accommodated the lack of clear-cut boundaries of poverty and its gradual nature. On the other hand, uncertainties related to lack of knowledge and imprecision in poverty data need also to be accounted for. The accuracy of poverty analysis is highly subject to how well these features are adequately addressed. We argue that possibility theory is an appropriate framework to deal with incomplete knowledge in poverty. Indeed, considering "the possibility of poverty" instead of the "probability of poverty" allows us to achieve a more realistic handling of this phenomenon. Empirical possibility distributions of monetary poverty states are derived based on our previous works and alpha-cut analysis is used to explore their features. Also, collective possibilistic poverty measures for each state are computed along with an aggregate possibilistic poverty ratio. This possibilistic modeling is applied to the analysis of poverty in Tunisia in 2005 and 2010.
The excess of zeros is a not a rare feature in count data. Statisticians advocate the Poisson-typ... more The excess of zeros is a not a rare feature in count data. Statisticians advocate the Poisson-type hurdle model (among other techniques) as an interesting approach to handle this data peculiarity. However, the frequency of gross errors and the complexity intrinsic to some considered phenomena may render this classical model unreliable and too limiting. In this paper, we develop a robust version of the Poisson hurdle model by extending the robust procedure for GLM (Cantoni and Ronchetti, 2001) to the truncated Poisson regression model. The performance of the new robust approach is then investigated via a simulation study, a real data application and a sensitivity analysis. The results show the reliability of the new technique in the neighborhood of the truncated Poisson model. This robust modelling approach is therefore a valuable complement to the classical one, providing a tool for reliable statistical conclusions and to take more effective decisions.
Fuzzy sets theory has successfully accommodated the lack of clear-cut boundaries of poverty and i... more Fuzzy sets theory has successfully accommodated the lack of clear-cut boundaries of poverty and its gradual nature. On the other hand, uncertainties related to lack of knowledge and imprecision in poverty data need also to be accounted for. The accuracy of poverty analysis is highly subject to how well these features are adequately addressed. We argue that possibility theory is an appropriate framework to deal with incomplete knowledge in poverty. Indeed, considering "the possibility of poverty" instead of the "probability of poverty" allows us to achieve a more realistic handling of this phenomenon. Empirical possibility distributions of monetary poverty states are derived based on our previous works and alpha-cut analysis is used to explore their features. Also, collective possibilistic poverty measures for each state are computed along with an aggregate possibilistic poverty ratio. This possibilistic modeling is applied to the analysis of poverty in Tunisia in 2005 and 2010.
Fuzzy conceptualization of privation has been a step closer to more realistic handling of poverty... more Fuzzy conceptualization of privation has been a step closer to more realistic handling of poverty. However, fuzzy approaches to poverty are still grounded on parametric axioms. Moreover, construction of poverty lines within these approaches still relies on ad-hoc methods. In this paper, we advance instead a fuzzy procedure based on the non-parametric bootstrap method, allowing us to depict fuzzy unidimensional privation states with boundaries drawn spontaneously from data. Fuzzy nonparametric measures of privation within each state as well as a collective fuzzy non-parametric index of poverty are derived, along with their corresponding confidence intervals. The new approach is applied to the analysis of poverty in Tunisia in 2005.
Journal of Statistical Planning and Inference, 2011
The excess of zeros is a not a rare feature in count data. Statisticians advocate the Poisson-typ... more The excess of zeros is a not a rare feature in count data. Statisticians advocate the Poisson-type hurdle model (among other techniques) as an interesting approach to handle this data peculiarity. However, the frequency of gross errors and the complexity intrinsic to some considered phenomena may render this classical model unreliable and too limiting. In this paper, we develop a robust version of the Poisson hurdle model by extending the robust procedure for GLM (Cantoni and Ronchetti, 2001) to the truncated Poisson regression model. The performance of the new robust approach is then investigated via a simulation study, a real data application and a sensitivity analysis. The results show the reliability of the new technique in the neighborhood of the truncated Poisson model. This robust modelling approach is therefore a valuable complement to the classical one, providing a tool for reliable statistical conclusions and to take more effective decisions.
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Papers by ASMA ZEDINI