Mean Squared Error of Estimation or Prediction under a General Linear Model

The problem considered is that of predicting a linear combination of the fixed and random effects of a mixed-effects linear model. More generally, the problem considered is that of predicting an unobservable random variable from a set of observable random variables. The best linear-unbiased predicto...

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Bibliographic Details
Published in:Journal of the American Statistical Association 1992-09, Vol.87 (419), p.724-731
Main Authors: Harville, David A., Jeske, Daniel R.
Format: Article
Language:English
Subjects:
Approximation
Best linear unbiased estimation
Best linear unbiased prediction
Empirical Bayes inference
Estimation bias
Estimation methods
Estimators
Exact sciences and technology
Expected values
Incomplete block designs
Linear inference, regression
Linear models
Mathematics
Maximum likelihood estimation
Mixed linear model
Probability and statistics
Random variables
Sciences and techniques of general use
Small-area estimation
Statistical variance
Statistics
Theory and Methods
Unbiased estimators
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Description
Summary:The problem considered is that of predicting a linear combination of the fixed and random effects of a mixed-effects linear model. More generally, the problem considered is that of predicting an unobservable random variable from a set of observable random variables. The best linear-unbiased predictor depends on parameters which generally are unknown. Various exact or approximate expressions are given for the mean squared error (MSE) of the predictor obtained by replacing the unknown parameters with estimates. Several estimators of the MSE are investigated.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.1992.10475274