Part CCSIR NET December 2023estimability-in-anova

Estimability in anova

Consider the one-way fixed effects ANOVA model $Y_{ij} = μ + α_{i} + ε_{ij}, j = 1, \dots, n_{i}; i = 1, \dots, k$ , with uncorrelated errors of mean 0 and variance $σ^{2}$ . Let Ȳ $_{i}$ be the i-th group mean. Which of the following statements are true?

A. $(1/ \sum n_{i}) \sum_{i} \sum_{j} Y_{ij}$ is an unbiased estimator of $μ$
B. $2 μ + α_{1} + α_{2}$ is an estimable linear parametric function
C. $μ + α_{1} + α_{2}$ is an estimable linear parametric function
D. $(1/ n_{2}) \sum_{j} (Y_{2 j} -$ Ȳ $_{2})$ is an unbiased estimator of $α_{2}$

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The trap it tests

Hypothesis dropped

A theorem applied without checking one of its preconditions.

Drill statements like this

Related counterexample: OLS is the BLUE in every linear model

Estimability in anova

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