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ANSC*6370 QG and Animal Models
Fall 03 - Quiz 5 - Answers

1.
Define the following terms in b.l.u.e.
best=
Minimizes the variance of errors of estimation.


linear=
Is a linear function of the observations, ${\bf L}'{\bf y}$.


unbiased=
Expected value of estimator equals expected value of estimand (quantities to be estimated).


estimator=
Estimator.








2.
Explain the differences between generalized least squares, ordinary least squares, and weighted least squares.

Generalized LS: \( {\bf X}'{\bf V}^{-1}{\bf X}\hat{\bf b}= {\bf X}'{\bf V}^{-1}{\bf y}. \)for ${\bf V}$ being a general covariance matrix.

Ordinary LS: \( {\bf X}'{\bf V}^{-1}{\bf X}\hat{\bf b}= {\bf X}'{\bf V}^{-1}{\bf y}. \)for ${\bf V }= {\bf I}\sigma^{2}$.

Weighted LS: \( {\bf X}'{\bf V}^{-1}{\bf X}\hat{\bf b}= {\bf X}'{\bf V}^{-1}{\bf y}. \)for ${\bf V}= $ any diagonal matrix with diagonals not all equal.



3.
The variance-covariance matrices of the random effects of a model are supposed to be symmetric and ???

Positive Definite.


Larry Schaeffer
2003-10-23