course | course_year | question_number | tags | title | year | |||
---|---|---|---|---|---|---|---|---|
Statistics |
IB |
74 |
|
Paper 1, Section II, E |
2010 |
Consider the the linear regression model
where the numbers
State and prove the Gauss-Markov theorem in the context of this model.
Write down the distribution of an arbitrary linear estimator for
$$\mathbb{E}{\beta, \sigma^{2}}\left[(\widehat{\beta}-\beta)^{4}\right] \leqslant \mathbb{E}{\beta, \sigma^{2}}\left[(\widetilde{\beta}-\beta)^{4}\right]$$
for all linear, unbiased estimators
[Hint: If