2016 Fiscal Year Final Research Report
Asymptotic properties of parameter estimators for quantitative methods in the behavioral sciences
| Project/Area Number |
26330031
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | Otaru University of Commerce |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | 項目反応理論 / 項目パラメータ / 能力の推定量 / 漸近的性質 / 漸近平均２乗誤差 / カノニカルパラメータ |
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| Outline of Final Research Achievements |
In quantitative methods for the behavioral sciences, asymptotic properties of the parameter estimators in statistical models are derived. In particular, for the 3-parameter logistic model, a typical model in ability tests using item response theory (IRT), the ability and item parameters are focused on, where the maximum likelihood and Bayes modal estimators of these parameters are used. In the case of ability estimation, the weighted score estimator is also dealt with, where the two cases of known and estimated item parameters are considered. As a general statistical method, an asymptotic bias adjustment of usual maximum likelihood estimators minimizing the asymptotic mean square error is obtained. This method has been applied to the estimation of ability in IRT.
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| Free Research Field |
統計科学
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