Reference : Smooth semiparametric and nonparametric Bayesian estimation of bivariate densities from ...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/69417
Smooth semiparametric and nonparametric Bayesian estimation of bivariate densities from bivariate histogram data
English
Lambert, Philippe mailto [Université de Liège - ULg > Institut des sciences humaines et sociales > Méthodes quantitatives en sciences sociales >]
2011
Computational Statistics & Data Analysis
Elsevier Science
55
429-445
Yes (verified by ORBi)
International
0167-9473
Amsterdam
The Netherlands
[en] Grouped data ; Bivariate density estimation ; Bayesian P-splines
[en] Penalized B-splines combined with the composite link model are used to estimate a bivariate density from a histogram with wide bins. The goals are multiple: they include the visualization of the dependence between the two variates, but also the estimation of derived quantities like Kendall’s tau, conditional moments and quantiles. Two strategies are proposed: the first one is semiparametric with flexible margins modeled using B-splines and a parametric copula for the dependence structure; the second one is nonparametric and is based on Kronecker products of the marginal B-spline bases. Frequentist and Bayesian estimations are described. A large simulation study quantifies the performances of the two methods under different dependence structures and for varying strengths of dependence, sample sizes and amounts of grouping. It suggests that Schwarz’s BIC is a good tool for classifying the competing models. The density estimates are used to evaluate conditional quantiles in two applications in social and in medical sciences.
FSR research grant No. FSRC-08/42 from the University of Liège ; IAP research network No. P6/03 of the Belgian government (Belgian Science Policy)
CREATION D’OUTILS STATISTIQUES POUR L’ANALYSE DE DONNEES D’ENQUETES CENSUREES PAR INTERVALLE
Researchers
http://hdl.handle.net/2268/69417
10.1016/j.csda.2010.05.011

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