By Hardeo Sahai

ISBN-10: 0817632298

ISBN-13: 9780817632298

Systematic therapy of the generally hired crossed and nested class types utilized in research of variance designs with a close and thorough dialogue of convinced random results types now not quite often present in texts on the introductory or intermediate point. it is usually numerical examples to research information from a wide selection of disciplines in addition to any labored examples containing desktop outputs from commonplace software program applications comparable to SAS, SPSS, and BMDP for every numerical instance.

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**Additional info for Analysis of Variance for Random Models, Volume 2: Unbalanced Data: Theory, Methods, Applications, and Data Analysis**

**Sample text**

14) and E(Lσ 2 σ 2 ) = − = − ∂ 2 V −1 1 ∂ 2 n|V | 1 tr E(Y − Xα)(Y − Xα) − 2 ∂σi2 ∂σj2 2 ∂σi2 ∂σj2 1 ∂ 2 n|V | 1 V ∂ 2 V −1 tr − 2 ∂σi2 ∂σj2 2 ∂σi2 ∂σj2 i, j = 1, . . , p. 16) 32 Chapter 10. 17) . 17), we obtain 2 ∂ 2 { n|V |} ∂V ∂V −1 ∂ V = tr V − V −1 2 V −1 2 2 2 2 2 ∂σi ∂σj ∂σi ∂σj ∂σj ∂σi . 18) with respect to σi2 , we obtain ∂ 2 V −1 ∂V ∂V ∂ 2V = V −1 2 V −1 2 V −1 − V −1 2 2 V −1 2 2 ∂σi ∂σj ∂σj ∂σi ∂σi ∂σj + V −1 ∂V −1 ∂V −1 V V . 20) by V and taking the trace yields tr V ∂ 2 V −1 ∂σi2 ∂σj2 = tr ∂ 2V ∂V −1 ∂V −1 V V − V −1 ∂σj2 ∂σi2 ∂σi2 ∂σj2 + ∂V −1 ∂V −1 V V ∂σi2 ∂σj2 = tr 2V −1 2 ∂V −1 ∂V −1 ∂ V .

N . Therefore, the estimator of σe2 is given by σˆ e2 = n i=1 (yi − y¯. )2 . 7) Again, the procedure leads to the usual unbiased estimator of σe2 . 6 ESTIMATION OF POPULATION MEAN IN A RANDOM EFFECTS MODEL In many random effects models, it is often of interest to estimate the population mean µ. For balanced data, as we have seen in Volume I, the “best’’ estimator of µ is the ordinary sample mean. However, for unbalanced data, the choice of a best estimator of µ is not that obvious. 5 that the SSP method involved the construction of an unbiased estimate of the square of the population mean.

A Theory Methods, 11, 1403–1425. R. Pringle and A. Raynor (1971), Generalized Inverse Matrices with Applications in Statistics, Hafner, New York. C. R. Rao and S. K. Mitra (1971), Generalized Inverse of Matrices and Its Applications, Wiley, New York. C. R. Rao and M. B. Rao (1998), Matrix Algebra and Its Applications to Statistics and Econometrics, World Scientiﬁc, Singapore. H. Scheffé (1959), The Analysis of Variance, Wiley, New York. J. R. Schott (1997), Matrix Analysis for Statistics, Wiley, New York.

### Analysis of Variance for Random Models, Volume 2: Unbalanced Data: Theory, Methods, Applications, and Data Analysis by Hardeo Sahai

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