An asymptotically unbiased estimator is a type of estimator that converges to the true value of the parameter being estimated as the sample size increases.
It is considered to be an ideal estimator because it does not suffer from bias or systematic error, and its performance does not deteriorate as the sample size increases.
How to calculate
- Specify the population of interest and the parameter being estimated.
- Collect a sample of data from the population of interest.
- Calculate the estimator (statistical measure) from the sample data.
- Compare the estimator to the true value of the estimated parameter.
- If the estimator converges to the true parameter value as the sample size increases, it is considered an asymptotically unbiased estimator.
Examples
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Maximum Likelihood Estimation, a common tool for estimating parameters in a statistical model, is an example of an asymptotically unbiased estimator.
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The method of moments, a method of estimating parameters based on the observed moments of a sample, is another example of an asymptotically unbiased estimator.
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The James-Stein estimator, a method of estimating parameters using a shrinkage technique, is yet another example of an asymptotically unbiased estimator.