James Stein Estimators
- Methods that improve the accuracy of point estimates compared with using raw sample means.
- The shrinkage estimator adjusts the sample mean by a shrinkage factor determined from the data’s variability.
- The empirical Bayes estimator adjusts sample means while accounting for different variances across observations.
Definition
Section titled “Definition”James-Stein estimators are statistical methods that are used to improve the accuracy of point estimates. These estimators are named after Charles James and William Stein, who first developed them in the 1950s.
Explanation
Section titled “Explanation”A James-Stein estimator modifies standard point estimates (such as the sample mean) by incorporating additional information about the data. In the shrinkage approach, the sample mean is adjusted by a shrinkage factor that depends on the variability of the data. In the empirical Bayes approach, the sample mean is adjusted while taking into account differing variances among data points. Both approaches aim to produce more accurate and reliable point estimates by accounting for variability in the data.
Examples
Section titled “Examples”Shrinkage estimator
Section titled “Shrinkage estimator”When there are multiple data points and their sample mean is calculated, the shrinkage estimator adjusts the sample mean by a certain amount, known as the shrinkage factor. This adjustment is based on the variability of the data and can improve the accuracy of the point estimate.
Empirical Bayes estimator
Section titled “Empirical Bayes estimator”When there are multiple data points with different variances, the empirical Bayes estimator adjusts the sample mean by taking into account the different variances of the data. This can improve the accuracy of the point estimate by accounting for the variability of the data.
Related terms
Section titled “Related terms”- Point estimates
- Sample mean
- Shrinkage estimator
- Empirical Bayes estimator