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2020 Nonparametric estimation of the ability density in the Mixed-Effect Rasch Model
Johanna Kappus, Friedrich Liese, Alexander Meister
Electron. J. Statist. 14(2): 2957-2987 (2020). DOI: 10.1214/20-EJS1736


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.


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Johanna Kappus. Friedrich Liese. Alexander Meister. "Nonparametric estimation of the ability density in the Mixed-Effect Rasch Model." Electron. J. Statist. 14 (2) 2957 - 2987, 2020.


Received: 1 January 2020; Published: 2020
First available in Project Euclid: 13 August 2020

zbMATH: 1448.62046
MathSciNet: MR4134349
Digital Object Identifier: 10.1214/20-EJS1736

Primary: 62B15, 62G07, 62G20


Vol.14 • No. 2 • 2020
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