Consider the model $y_{ij} = \mu + \alpha_i +
\epsilon_{ij},$ where $i=1,2,3$ and $j=1,...,5.$ We
assume the Gauss-Markov set up. State with reason which of the
following parametric functions are estimable:
$\alpha_1-\alpha_3$
$\mu+\alpha_1$
$\mu-\alpha_2$
$\alpha_1-2 \alpha_2+\alpha_3$
Same set up as above. Is it true that all parametric
functons of the form $\sum_i c_i \alpha_i$ with $\sum c_i
= 0$, are estimable. Also, is it true that all such parametric
functons must be non-estimable if $\sum c_i\neq 0?$
Consider the Gauss-Markovian linear model $y_{ijk} = \mu +
\alpha_i + \beta_j + \epsilon_{ijk},$ where $i=1,...,I$
and $j=1,..,J$ and $k=1,...,n_{ij} (\geq 2).$ State with reason which of the
following parametric functions are estimable:
$\alpha_i-\alpha_j$ for $i\neq j.$
$\alpha_i+\alpha_j$ for $i\neq j.$
$\beta_i-\beta_j$ for $i\neq j.$
$\mu+\alpha_i$
$\mu-\alpha_i$
$\mu+\beta_j$
$\mu+\alpha_1+\beta_2$
Same set up as in the last problem.
If $\mu + \sum c_i \alpha_i$ is estimable:, then what
can you say about $c_i$'s?
If $\sum c_i \alpha_i$ is estimable:, then what
can you say about $c_i$'s?
If $\mu + \sum c_i \alpha_i + \sum d_j \beta_j$ is estimable:, then what
can you say about $c_i$'s and $d_j$'s?
Same set up as above. Find the dimension of the space of all
identifiable linear parametric functions. How does the answer
change if all the $n_{ij}$'s are known to be equal?