Empirical likelihood confidence regions for comparison distributions and roc curves

Abstract: The authors derive empirical likelihood confidence regions for the comparison distribution of two populations whose distributions are to be tested for equality using random samples. Another application they consider is to ROC curves, which are used to compare measurements of a diagnostic test from two populations. The authors investigate the smoothed empirical likelihood method for estimation in this context, and empirical likelihood based confidence intervals are obtained by means of the Wilks theorem. A bootstrap approach allows for the construction of confidence bands. The method is illustrated with data analysis and a simulation study. Resume: Les auteurs deduisent de la vraisemblance empirique des regions de confiance pour la distribution comparee de deux populations dont on veut tester l'egalite en loi au moyen d'echantillons aleatoires. Une autre application qu'ils considerent concerne les courbes ROC, qui permettent de comparer les resultats d'un test diagnostique effectue aupres de deux populations. L'estimation proposee par les auteurs dans ce contexte s'appuie sur une methode de lissage de la vraisemblance empirique qui conduit, grǎce au theoreme de Wilks, aux intervalles de confiance recherches. Une approche bootstrap permet en outre de construire des bandes de confiance. La methode est illustree au moyen de simulations et d'un jeu de donnees.

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