Estimator
In statistics, an estimator is a rule for calculating an estimate of a given amount based on observed data. The rule (the estimator), the amount that is being measured (the estimand) and its result (the estimate) are different.[1]
An estimator of a parameter [math]\displaystyle{ \theta }[/math] is often written as [math]\displaystyle{ \hat\theta }[/math].[2] If the expected value of the estimator is equal to the parameter, then the estimator is called unbiased. Otherwise, it is called biased.[3]
Estimator Media
An estimate is not the same thing as an estimator: an estimate is a specific value dependent on only the dataset while an estimator is a method for estimation that is realized through random variables.
Difference between estimators: an unbiased estimator \theta_2 is centered around \theta vs. a biased estimator \theta_1.
A estimator curve the has high frequency accumulated at the center and low frequency on two sides
A bad estimator example
Comparison between good and bad estimator
Related pages
References
- ↑ Mosteller, F.. The Collected Works of John W. Tukey: Philosophy and Principles of Data Analysis 1965–1986 4 (1987)CRC Press. p. 601–720 [p. 633]. ISBN 0-534-05101-4.
- ↑ List of Probability and Statistics Symbols (in en-US). Math Vault (2020-04-26). Retrieved 2020-09-12.
- ↑ Taylor, Courtney. Unbiased and Biased Estimators (in en). ThoughtCo (January 13, 2019). Retrieved 2020-09-12.
Other websites
- Fundamentals on Estimation Theory Archived 2020-02-12 at the Wayback Machine