Teaching CSIR NET Mock Test Series Mathematical Science Statistics & Exploratory Data Analysis Methods of Estimation
Consider the one-way fixed effects ANOVA model
Yij = μ + αi + εij, j = 1, ..., ni; i = 1, ..., k,
where the errors εij s are uncorrelated with mean 0 and finite variance σ2(> 0). Let \(\bar{Y}_i=\frac{1}{n_i} \sum_{j=1}^{n_i} Y_{i j}\) for i = 1, .., k. Then, which of the following statements are true?
1
\(\frac{1}{\sum_{i=1}^k n_i} \sum_{i=1}^k \sum_{j=1}^{n_i} Y_{i j}\) is an unbiased estimator of μ
2
2 μ + α1 + α2 is an estimable linear parametric function
3
μ + α1 + α2 is an estimable linear parametric function
4
\(\frac{1}{n_2} \sum_{j=1}^{n_2}\left(Y_{2 j}-\bar{Y}_2\right)\) is an unbiased estimator of α2