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May 2019 Strong Gaussian approximation of the mixture Rasch model
Friedrich Liese, Alexander Meister, Johanna Kappus
Bernoulli 25(2): 1326-1354 (May 2019). DOI: 10.3150/18-BEJ1022

Abstract

We consider the famous Rasch model, which is applied to psychometric surveys when $n$ persons under test answer $m$ questions. The score is given by a realization of a random binary $n\times m$-matrix. Its $(j,k)$th component 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 persons are chosen randomly from a 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.

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Friedrich Liese. Alexander Meister. Johanna Kappus. "Strong Gaussian approximation of the mixture Rasch model." Bernoulli 25 (2) 1326 - 1354, May 2019. https://doi.org/10.3150/18-BEJ1022

Information

Received: 1 February 2017; Revised: 1 August 2017; Published: May 2019
First available in Project Euclid: 6 March 2019

zbMATH: 07049408
MathSciNet: MR3920374
Digital Object Identifier: 10.3150/18-BEJ1022

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

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Vol.25 • No. 2 • May 2019
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