Minimum Aberration Criterion
- Compares estimators by the expected deviation between the estimator and the true parameter.
- Selects the estimator that yields the smallest expected “aberration”.
- Useful for choosing among practical estimators when full measurement is infeasible.
Definition
Section titled “Definition”The minimum aberration criterion is a method used to evaluate and compare the performance of statistical estimators. It is based on the idea that the best estimator is the one that minimizes the expected value of the deviation or “aberration” between the estimator and the true value of the parameter being estimated.
Explanation
Section titled “Explanation”- The criterion evaluates estimators by computing their expected deviation from the true parameter value and prefers the estimator with the smallest expected deviation.
- It applies when full measurement of a population is impractical and an estimator based on a sample must be used; careful choice of estimator and sample can reduce the expected aberration.
- To apply the criterion, compare the expected deviations of candidate estimators (for example, mean versus median) and choose the estimator whose expected deviation from the true parameter is smaller.
Examples
Section titled “Examples”Estimating average height from a sample
Section titled “Estimating average height from a sample”- Measuring the height of every person in a group gives a very accurate estimate but can be time-consuming and impractical for large groups.
- A practical alternative is to select a random sample and estimate the average from that sample.
- Example given: to estimate the average height of a group of 100 people using a sample of 10 people, compare estimators (e.g., the mean and the median) by calculating the expected deviation between each estimator and the true average. If the mean has a smaller expected deviation than the median, the mean would be chosen under the minimum aberration criterion.
Use cases
Section titled “Use cases”- Tool for statisticians and researchers who need to make accurate estimates based on limited data.
Notes or pitfalls
Section titled “Notes or pitfalls”- Measuring an entire population is more accurate but may be impractical; the criterion explicitly addresses the trade-off between accuracy and practicality.
- The quality of the estimator under this criterion depends on how well the expected deviation is assessed and on sample selection.
Related terms
Section titled “Related terms”- Estimator
- Mean
- Median
- Expected value
- Parameter
- Sample