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- PublicationMétadonnées seulement
- PublicationMétadonnées seulementPolicy Recommendations and Methodological Report(Trier University of Trier, 2011)
; ; - PublicationMétadonnées seulementDiscretizing a compound distribution with application to categorical modelling(2017-2-17)
; 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 define a partition of the domain of definition of the random parameters, so that we can represent the expected density of the variable of interest as a finite mixture of conditional densities. We then model the mixture probabilities of the conditional densities using information on population categories, thus modifying the original overall model. We thus obtain specific models for sub-populations that stem from the overall model. The distribution of a sub-population of interest is thus completely specified in terms of mixing probabilities. All characteristics of interest can be derived from this distribution and the comparison between sub-populations easily proceeds from the comparison of the mixing probabilities. A real example based on EU-SILC data is given. Then the methodology is investigated through simulation. - PublicationMétadonnées seulement
- PublicationMétadonnées seulementGeneral framework for the rotation of units in repeated survey sampling(2009-3-23)
; ; Coordination of probabilistic samples is a challenging theoretical problem faced by statistical institutes. One of their aims is to obtain good estimates for each wave while spreading the response burden across the entire population. There is a collection of existing solutions that try to attend to these needs. These solutions, which were developed independently, are integrated in a general framework and their corresponding longitudinal designs are computed. The properties of these longitudinal designs are discussed. It is also noted that there is an antagonism between a good rotation and control over the cross-sectional sampling design. A compromise needs to be reached between the quality of the sample coordination, which appears to be optimal for a systematic longitudinal sampling design, and the freedom of choice of the cross-sectional design. In order to reach such a compromise, an algorithm that uses a new method of longitudinal sampling is proposed. - PublicationAccès libreSampling Procedures for Coordinating Stratified Samples : Methods Based on MicrostrataThe aim of sampling coordination is to maximize or minimize the overlap between several samples drawn successively in a population that changes over time. Therefore, the selection of a new sample will depend on the samples previously drawn. In order to obtain a larger (or smaller) overlap of the samples than the one obtained by independent selection of samples, a dependence between the samplesmust be introduced. This dependence will emphasize (or limit) the number of common units in the selected samples. Several methods for coordinating stratified samples, such as the Kish & Scott method, the Cotton & Hesse method, and the Rivi`ere method, have already been developed. Using simulations, we compare the optimality of these methods and their quality of coordination. We present six new methods based on permanent random numbers (PRNs) and microstrata. These new methods have the advantage of allowing us to choose between positive or negative coordination with each of the previous samples. Simulations are run to test the validity of each of them.
- PublicationMétadonnées seulement
- PublicationMétadonnées seulementParametric modelling of income and indicators of poverty and social exclusion from EU-SILC data and simulated universe(2011-5-23)
; In the context of the AMELI project, we aim at developing reliable and efficient methodologies for the estimation of a certain set of indicators, computed within the EU-SILC survey, i.e. the median, the at-risk-of-poverty rate (ARPR), the relative median poverty gap (RMPG), the quintile share ratio (QSR) and the Gini index. The reason why parametric estimation may be useful when empirical data and estimators are available is threefold: 1. to stabilize estimation; 2. to get insight into the relationships between the characteristics of the theoretical distribution and a set of indicators, e.g. by sensitivity plots; 3. to deduce the whole distribution from known empirical indicators, when the raw data are not available. Special emphasis is laid on the Generalized Beta distribution of the second kind (GB2), derived by McDonald (1984). Apart from the scale parameter, this distribution has three shape parameters: the first governing the overall shape, the second the lower tail and the third the upper tail of the distribution. These characteristics give to the GB2 a large flexibility for fitting a wide range of empirical distributions and it has been established that it outperforms other four-parameter distributions for income data (Kleiber and Kotz, 2003). We have studied different types of estimation methods, taking into account the design features of the EU-SILC surveys. Pseudo-maximum likelihood estimation of the parameters is compared with a nonlinear fit from the indicators. Variance estimation is done by linearization and different types of simplified formulas for the variance proposed in the literature are evaluated by simulation. The GB2 can be represented as a compound distribution, the compounding parameter being the scale parameter. We use this property to decompose the GB2 distribution into a mixture of component distributions, to refine the GB2 fit of the income variable for subgroups and to ameliorate the GB2 estimates of the indicators. Computations are made on the synthetic universe AMELIA constructed from the EU-SILC data (Alfons et al., 2011) and the simulation is done with the R package SimFrame (Alfons, A., 2010). Both AMELIA and SimFrame are developed in the context of the AMELI project. The parametric methods we have developed are made available in the R package GB2, which is part of the output of the AMELI project. Ref: 1) AMELIwebsite 2) Alfons, A. (2010). simFrame: Simulation framework. R package version 0.2. URL http://CRAN.R-project.org/package=simFrame. 3) Alfons, A., Templ, M., Filzmoser, P., Kraft, S., Hulliger, B., Kolb, J.-P., and Münnich, R. (2011). Synthetic data generation of SILC data. Deliverable 6.2. of the Ameli project. 4) Graf, M. and Nedyalkova, D. (2010). GB2: Generalized Beta Distribution of the Second Kind: properties, likelihood, estimation. R package version 1.0. 5) Kleiber, C. and Kotz, S. (2003). Statistical Size Distributions in Economics and Actuarial Sciences. John Wiley & Sons, Hoboken, NJ.