Download Analysis of Variance for Random Models, Volume 2: Unbalanced by Hardeo Sahai PDF

By Hardeo Sahai

Systematic therapy of the generally hired crossed and nested type types utilized in research of variance designs with a close and thorough dialogue of convinced random results versions no longer as a rule present in texts on the introductory or intermediate point. it is usually numerical examples to investigate information from a wide selection of disciplines in addition to any labored examples containing computing device outputs from ordinary software program programs corresponding to SAS, SPSS, and BMDP for every numerical instance.

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

Sample text

1) where E(µˆ 2 ) = E{Q(Y )} = µ2 . Now, consider the set of transformations on the data obtained by adding a constant θ to each observation. After making such a transformation, the SSP method is used to obtain the unbiased estimator of the square of the population mean of the transformed data, which will have the form Q(Y + θ1). Then it follows that 2 (µ + θ ) = Q(Y + θ1) = Q(Y ) + 2G(Y )θ + θ 2 , where G(Y ) is a linear function of the observations. 2) 26 Chapter 10. 2) is (µˆ − G(Y ))2 = Q(Y ) − {G(Y )}2 = µˆ 2 − {G(Y )}2 .

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. S. R. Searle (1971), Linear Models, Wiley, New York. S. R. Searle (1982), Matrix Algebra Useful for Statistics, Wiley, New York. S. R. , Comm.

The methods were critically reviewed and reformulated in elegant matrix notations by Searle (1968). Since then a bewildering variety of new procedures have been developed and the theory has been extended in a number of different directions. The principal developments include the adoption of an old and familiar method of maximum likelihood and its variant form, the socalled restricted maximum likelihood to the problem of variance components estimation. In addition, C. R. Rao (1970, 1971a, 1972) introduced the concept of minimum-norm quadratic unbiased estimation (MINQUE).

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