Strong Gaussian approximation of the mixture Rasch model
schedule le mardi 21 novembre 2017 de 10h45 à 11h45
Organisé par : I. Castillo, A. Fischer, E. Roquain, M. Sangnier
Intervenant : Alexander Meister (University of Rostock)
Lieu : UPMC, salle 15-16.201
Sujet : Strong Gaussian approximation of the mixture Rasch model
We consider the famous Rasch model, which is applied to psychometric surveys when n individuals under test answer m questions. The score is given by a realization of a random binary matrix. Its (j,k)-th entry indicates whether or not the answer of the j-th person to the k-th question is correct. In the mixture Rasch model one assumes that the individuals are chosen randomly from a huge population. We prove that the mixture Rasch model is asymptotically equivalent to a Gaussian observation scheme in Le Cam's sense as n tends to infinity and m is allowed to increase slowly in n. For that purpose we show a general result on strong Gaussian approximation of the sum of independent high-dimensional binary random vectors. As a first application we construct an asymptotic confidence region for the difficulty parameters of the questions. Moreover we discuss nonparametric estimation of the ability density. This talk is based on a joint work with F. Liese and J. Kappus (Univ. Rostock).