The main objective of the study is to compare the Newton–Cotes methods such as the Trapezium rule, Simpson 1/3 rule and Simpson 3/8 rule to estimate the area under the Lorenz curve and Gini coefficient of income using polynomial function with degree 5. Comparing the Gini coefficients of income computed from the Polynomial function with degree 5 for the Trapezium, Simpson 1/3 and Simpson 3/8 methods using the relative errors showed that the trapezium rule, Simpson’s 1/3 rule and Simpson’s 3/8 rule show negative biases with the Simpson 1/3 rule yielding the lowest absolute relative true error of 4.230711 %.
Abstract. This paper considers the problem of networks reconstruction from heterogeneous data using a Gaussian Graphical Mixture Model (GGMM). It is well known that parameter estimation in this context is challenging due to large numbers of variables coupled with the degenerate nature of the likelihood. We propose as a solution a penalized maximum likelihood technique by imposing an l 1 penalty on the precision matrix. Our approach shrinks the parameters thereby resulting in better identifiability and variable selection.Résumé. Cet article considère le problème de la reconstruction de réseauxà partir de données hétérogènes en utilisant le modèle graphique gaussien mémangé (GGMM en Anglais). Il est connu que l'estimation paramétrique, dans ce contexte, n'est pas aiséà cause du grand nombre de variable et de la nature dégénérée de la vraisemblance. Nous proposons comme une solution une méthode de pénalisation du maximum de vraisemblance en imposant une pénalité de type L1 sur la précision de la matrice. Notre méthode réduit les paramètres et ainsi aboutità une meilleure identification età un meilleur choix des variables. .
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