In a variance component model,(Formula presented.), Pukelsheim (1981) proved that the non-negative and unbiased estimation of the variance components σ(Formula presented.), j=1, …, c, entails a transformation of the original model to Q(Formula presented.) (called Q-reduced model). The maximum likelihood (ML) approach based on the likelihood of Q(Formula presented.) (denoted Q-ML) is considered and applied to an incomplete block design (IBD) model. The Q-ML estimators of variance components and are shown to be more efficient in the mean squared error sense than the non-negative MINQUE’s (minimum norm quadratic unbiased estimators) in the IBD. The effect of using Q-ML estimators of the variance components to estimate the variance ratio in the combined estimator of the treatment contrast is also considered.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-13429 |
| Date | 01 January 1988 |
| Creators | Lee, K. R., Kapadia, C. H. |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Detected Language | English |
| Type | text |
| Source | ETSU Faculty Works |
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