Download e-book for iPad: Analysis of Variance for Random Models, Volume 2: Unbalanced by Hardeo Sahai

By Hardeo Sahai

ISBN-10: 0817632298

ISBN-13: 9780817632298

Systematic therapy of the generally hired crossed and nested type types utilized in research of variance designs with a close and thorough dialogue of definite random results versions no longer ordinarily present in texts on the introductory or intermediate point. it is usually numerical examples to investigate facts from a wide selection of disciplines in addition to any labored examples containing laptop outputs from ordinary software program programs akin 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

Example text

Ii) While it is true that the procedure yields a sequence estimator with the usual asymptotic properties of maximum likelihood estimators, it is hard to justify the choice of an estimator on the basis of its being a part of a “good’’ sequence. (iii) The amount of computation required to apply the Hartley–Rao procedure may be undesirable or prohibitively large. (iv) The sampling distribution of the estimates produced by the Hartley–Rao procedure can usually be investigated only by a Monte Carlo method.

It appears likely that the “goodness’’ of their estimates is directly related to the goodness of their starting values. 2 LARGE SAMPLE VARIANCES General expressions for large sample variances of the ML estimators of variance components can be derived, even though the estimators themselves cannot be obtained explicitly. Thus it is known that the large sample variance-covariance matrix of the ML estimators of any model is the inverse of the information matrix. , Wald, 1943). The above results can be utilized in deriving large sample variances and covariances of the ML estimators.

Tr ⎢ ⎣ ⎪ ⎪ . ⎩ 0 .. X2 [I − X1 (X1 X1 )− X1 ]X2 ⎡ ⎤⎫ .. ⎬ E(β1 β1 ) . E(β1 β2 ) ⎦ ×⎣ . ⎭ E(β2 β1 ) .. E(β2 β2 ) ⎤ ⎥ ⎥ ⎦ + σe2 [rank(X) − rank(X1 )] = tr{X2 [I − X1 (X1 X1 )− X1 ]X2 E(β2 β2 )} + σe2 [rank(X) − rank(X1 )]. 12) is a function only of E(β2 β2 ) and σe2 and has been derived without any assumption on the form of E(ββ ). 12) states that if the vector β is partitioned as (β1 , β2 ), where β1 represents all the fixed effects and β2 represents all the random effects, then E{R(β2 |β1 )} contains only σe2 and the variance components associated with the random effects; it contains no terms due to the fixed effects.

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

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