Part CCSIR NET December 2024a-saturated-model-leaves-no-choice-of-estimator

A saturated model leaves no choice of estimator

Consider a linear model $Y_{i} = β_{1} + β_{2} + \dots + β_{i} + ε_{i}, 1 \leq i \leq n$ , where the errors $ε_{i}^{'} s$ are uncorrelated with zero mean and finite variance $σ^{2} > 0$ . Then, which of the following statements are true?

A.Every linear function of $β_{i}, 1 \leq i \leq n$ , is not estimable.
B.Every $β_{i}, 1 \leq i \leq n$ , has infinitely many linear unbiased estimators, but a unique best linear unbiased estimator.
C.Each $β_{i}, 1 \leq i \leq n$ , has only one linear unbiased estimator.✓
D. $Y_{2} - Y_{1}$ is the best linear unbiased estimator of $β_{2}$ .✓

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

See pricing

50 are analysed free — try those first.

Related counterexample: OLS is the BLUE in every linear model

A saturated model leaves no choice of estimator

More on this topic