Download e-book for iPad: Analysis of variance for random models, vol.2: Unbalanced by Sahai H., Ojeda M.M.

By Sahai H., Ojeda M.M.

ISBN-10: 0817632298

ISBN-13: 9780817632298

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Additional resources for Analysis of variance for random models, vol.2: Unbalanced data

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1 HENDERSON’S METHOD I Of the three methods of Henderson, Method I is the easiest to compute and is probably the most frequently used method of estimation of variance components. The procedure involves evaluating sums of squares analogous to those used for the analysis of variance for balanced data. These are then equated to their respective expected values and solved for variance components. 1) following closely the developments given in Searle (1971b, pp. 431–434). In subsequent chapters, we discuss the application of the method for special cases.

Recently, Westfall (1986) has shown that Henderson’s Method I estimators of variance components in the nonnormal unbalanced hierarchical mixed model are asymptotically normal. In particular, Westfall (1986) provides conditions under which the ANOVA estimators from a nested mixed model have an asymptotic multivariate normal distribution. 1) where α represents all the fixed effects except that the general constant µ and β represents all the random effects. 2. 2) where µ∗ is a new scalar and e∗ = (I − XL)e is an error vector different from e.

N2 . The problem is to estimate σi2 s when they may be all unequal. C. R. Rao (1970) derived the conditions on X which ensure unbiased estimability of the σi2 s. He further introduced an estimation principle, called the minimum-norm quadratic unbiased estimation (MINQUE), and showed that the estimators of Hartley et al. (1969) are in fact MINQUE. As noted by Rao (1972), the problem of estimation of heteroscedastic variances is, indeed, a special case of the estimation of variance components problem.

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Analysis of variance for random models, vol.2: Unbalanced data by Sahai H., Ojeda M.M.


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