Chapter Contents |
Previous |
Next |

The Four Types of Estimable Functions |

For linear models such as

A linear combination of the parameters is estimable if and only if a linear combination of theAny linear combination of theYs exists that has expected value .

is estimable if and only if there is a linear combination of the rows ofThus, the rows ofXthat is equal toL-that is, if and only if there is aKsuch thatL=KX.

Therefore, if **L** can be written as a linear
combination of the rows of **X**, **X'X**,
or (**X'X**)^{-}**X'X**, then
is estimable.

Once an estimable **L** has been
formed,
can be estimated by computing **Lb**, where
**b** = (**X'X**)^{-}**X'Y**.
From the general theory of linear models, the unbiased estimator **Lb** is,
in fact, the *best* linear unbiased estimator of in the sense of having minimum variance as well as maximum likelihood
when the residuals are normal.
To test the hypothesis that , compute SS
and form an *F* test using the appropriate error term.

Chapter Contents |
Previous |
Next |
Top |

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.