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Graf, Monique
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Graf, Monique
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- PublicationMétadonnées seulementEstimation of poverty indicators in small areas under skewed distributions(2014)
; - PublicationMétadonnées seulementRegression for Compositions based on a Generalization of the Dirichlet DistributionConsider a positive random vector following a compound distribution where the compounding parameter multiplies non-random scale parameters. The associated composition is the vector divided by the sum of its components. The conditions under which the composition depends on the distribution of the compounding parameter are given. When the original vector follows a compound distribution based on independent Generalized Gamma components, the Simplicial Generalized Beta (SGB) is the most general distribution of the composition that is invariant with respect to the distribution of the compounding parameter. Some properties and moments of the SGB are derived. Conditional moments given a sub-composition give a way to impute missing parts when knowing a sub-composition only. Distributional checks are made possible through the marginal distributions of functions of the parts that should be Beta distributed. A multiple SGB regression procedure is set up and applied to data from the United Kingdom Time Use survey.
- PublicationMétadonnées seulementUse of survey weights for the analysis of compositional dataThis chapter contains sections titled: - Introduction - Elements of Survey Design - Application to Compositional Data - Discussion - References
- PublicationMétadonnées seulementLa variance sous calage: Mode d’emploi la macro SURVEYCALLa macro SAS SURVEYCAL, programmée par Monique Graf, est le résultat d’un mandat confié à l’Institut de statistique de l’université de Neuchâtel par la section METH de l’Office fédéral de la statistique. Il s’agit d’étendre au cas du calage sur marges les résultats fournis par la procédure SAS SURVEYMEANS. Cette procédure procure des méthodes d’estimation basée sur le plan d’échantillonnage, dans le cas d’une enquête basée sur un plan de taille fixe (stratifié en grappes). SURVEYCAL permet de traiter pratiquement tous les cas envisagés dans SURVEYMEANS. Ce document est d’abord un mode d’emploi de SURVEYCAL. S’y rajoutent des illustrations utilisant des données provenant de l’enquête SILC 2009 et quelques recommandations pour choisir la méthode de calage d’une part et le mode de calcul de la variance par linéarisation, d’autre part. On introduit une méthode originale pour le calcul des bornes de calage dans les cas linéaire tronqué et logit.
- PublicationMétadonnées seulementEchantillons à usage public des recensements suisse de la population 1970-2000(Neuchâtel Office fédéral de la statistique, 2005)
; - PublicationMétadonnées seulementEnquête suisse sur la structure des salaires. Programmes R pour l'intervalle de confiance de la médianeCe rapport comporte deux parties. La première, plus mathématique, présente les calculs effectués dans le cadre de la LSE: la méthode suivie pour le calcul de la médiane, les différentes étapes nécessaires pour établir un intervalle de confiance à 95% et trois coefficients de variation ainsi que le traitement des domaines sont décrits. La deuxième partie décrit chaque élément du programme qui a été implémenté. Puis, les fonctions du package survey ayant un rapport avec les méthodes de la LSE sont analysées. Pour terminer, une comparaison des performances du programme et du package est présentée.
- PublicationMétadonnées seulementWeighted distributionsIn a super-population statistical model, a variable of interest, defined on a finite population of size N, is considered as a set of N independent realizations of the model. The log-likelihood at the population level is then written as a sum. If only a sample is observed, drawn according to a design with unequal inclusion probabilities, the log-pseudo-likelihood is the Horvitz-Thompson estimate of the population log-likelihood. In general, the extrapolation weights are multiplied by a normalization factor, in such a way that normalized weights sum to the sample size. In a single level design, the value of estimated model parameters are unchanged by the scaling of weights, but it is in general not the case for multi-level models. The problem of the choice of the normalization factors in cluster sampling has been largely addressed in the literature, but no clear recommendations have been issued. It is proposed here to compute the factors in such a way that the pseudo-likelihood becomes a proper likelihood. The super-population model can be written equivalently for the variable of interest or for a transformation of this variable. It is shown that the pseudo-likelihood is not invariant by transformation of the variable of interest.
- PublicationMétadonnées seulement
- PublicationMétadonnées seulementDiscretizing a compound distribution with application to categorical modelling. Part I: Methods(Neuchâtel Université de Neuchâtel Institut de Statistique, 2014)
; Many probability distributions can be represented as compound distributions. Consider some parameter vector as random. The compound distribution is the expected distribution of the variable of interest given the random parameters. Our idea is to de_ne a partition of the domain of de_nition of the random parameters, so that we can represent the expected density of the variable of interest as a _nite mixture of conditional densities. We then model the probabilities of the conditional densities using information on population categories, thus modifying the original overall model. Our examples uses the European Union Statistics on Income and Living Conditions (EU-SILC) data. For each country, we estimate a mixture model derived from the GB2 in which the probability weights are predicted with household categories. Comparisons across countries are processed using compositional data analysis tools. Our method also o_ers an indirect estimation of inequality and poverty indices. - PublicationMétadonnées seulementSGB R-package Simplicial Generalized Beta RegressionPackage SGB contains a generalization of the Dirichlet distribution, called the Simplicial Generalized Beta (SGB). It is a new distribution on the simplex (i.e. on the space of compositions or positive vectors with sum of components equal to 1). The Dirichlet distribution can be constructed from a random vector of independent Gamma variables divided by their sum. The SGB follows the same construction with generalized Gamma instead of Gamma variables. The Dirichlet exponents are supplemented by an overall shape parameter and a vector of scales. The scale vector is itself a composition and can be modeled with auxiliary variables through a log-ratio transformation.