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Lesson 7 of 22 · 13 min
Good estimators, and the CLT across sampling designs
A good estimator is unbiased, efficient, consistent and, when the data are messy, robust; and how fast the sample mean becomes normal depends on the population's shape and on how the sample was drawn.
In short
- Unbiased: the estimator's expected value equals the parameter. The sample mean is unbiased for .
- MVUE (minimum-variance unbiased estimator): unbiased with the smallest variance of all unbiased estimators. BLUE (best linear unbiased estimator): the most efficient among unbiased estimators that are linear combinations of the data.
- Consistent: converges to the true value as n grows. Robust: stays reliable with outliers or non-normal data, for example a trimmed mean.
- Sample size the CLT needs: about 4–5 for symmetric, single-peaked populations; 25–30 for skewed ones; more for extreme skew.
- Stratified: the CLT works within each stratum and for the combined mean. Cluster: it depends on the size of the clusters, not the number of clusters. Non-probability samples: the CLT does not reliably apply.
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