Nonparametric estimation of the ability density in the Mixed-Effect Rasch Model
| Autor: | Alexander Meister, Friedrich Liese, Johanna Kappus |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
education.field_of_study minimax optimality Rasch model Population Nonparametric statistics item response theory Inverse problem symbols.namesake Operator (computer programming) statistical linear inverse problems Item response theory symbols 62G07 Applied mathematics Asymptotic equivalence Statistics Probability and Uncertainty Le Cam distance education Equivalence (measure theory) Gaussian network model 62G20 Mathematics 62B15 |
| Zdroj: | Electron. J. Statist. 14, no. 2 (2020), 2957-2987 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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