Bounds on variances of estimators for multinomial processing tree models |
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| Authors: | Pierre Baldi |
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| Affiliation: | a Department of Information and Computer Science, California Institute for Telecommunications and Information Technology, University of California, Irvine, CA 92697-3425, USAb School of Social Sciences, Institute for Mathematical Behavioral Sciences, University of California, Irvine, CA 92697-5100, USA |
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| Abstract: | When there are order constraints among the parameters of a binary, multinomial processing tree (MPT) model, methods have been developed for reparameterizing the constrained MPT into an equivalent unconstrained MPT. This note provides a theorem that is useful in computing bounds on the estimator variances for the parameters of the constrained model in terms of estimator variances of the parameters of the unconstrained model. In particular, we show that if X and Y are random variables taking values in [0,1], then Var[XY]?2(Var[X]+Var[Y]). |
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| Keywords: | Multinomial processing tree models Parametric order constraints Estimator variances Reparameterization |
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