The Rasch model is widely used in the field of psychometrics when $n$ persons under test answer $m$ questions and the score, which describes the correctness of the answers, is given by a binary $n\times m$-matrix. We consider the Mixed-Effect Rasch Model, in which the persons are chosen randomly from a huge population. The goal is to estimate the ability density of this population under nonparametric constraints, which turns out to be a statistical linear inverse problem with an unknown but estimable operator. Based on our previous result on asymptotic equivalence to a two-layer Gaussian model, we construct an estimation procedure and study its asymptotic optimality properties as $n$ tends to infinity, as does $m$, but moderately with respect to $n$. Moreover numerical simulations are provided.
"Nonparametric estimation of the ability density in the Mixed-Effect Rasch Model." Electron. J. Statist. 14 (2) 2957 - 2987, 2020. https://doi.org/10.1214/20-EJS1736