On equivalence of predictors/estimators under a multivariate general linear model with augmentation. (English) Zbl 1377.62143
Summary: Assume that a true multivariate general linear model for an observed random matrix is over-parameterized by adding some new regressors due to model uncertainty. Then predictors and estimators of parameter spaces in the true and over-parameterized models are not necessarily the same. In this article, we study the comparison problem of predictors/estimators of parameter spaces under the two models. In particular, we derive necessary and sufficient conditions for the best linear unbiased predictors/best linear unbiased estimators of the parameter spaces to be equivalent under the two models.
MSC:
| 62H12 | Estimation in multivariate analysis |
| 62J05 | Linear regression; mixed models |
| 62F30 | Parametric inference under constraints |
| 62J10 | Analysis of variance and covariance (ANOVA) |
Keywords:
true model; over-parameterized model; parametric functions; Kronecker product; BLUP; BLUE; multivariate general linear model; best linear unbiased predictor; best linear unbiased estimatorReferences:
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