Shrinkage Estimator

A Shrinkage Estimator is an estimator that shrinks the raw estimate.

• See: Statistical Inference, Statistics, Estimator, Shrinkage (Statistics), Regularization (Mathematics), Ill-Posed Problem.

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References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/shrinkage_estimator Retrieved:2015-5-11.
  • In statistics, a shrinkage estimator is an estimator that, either explicitly or implicitly, incorporates the effects of shrinkage. In loose terms this means that a naive or raw estimate is improved by combining it with other information. The term relates to the notion that the improved estimate is made closer to the value supplied by the 'other information' than the raw estimate. In this sense, shrinkage is used to regularize ill-posed inference problems.

2017

• http://www.statisticshowto.com/shrinkage-estimator/ Retrieved:2017-10-27.
  • A shrinkage estimator is a new estimate produced by shrinking a raw estimate (like the sample mean). For example, two extreme mean values can be combined to make one more centralized mean value; repeating this for all means in a sample will result in a revised sample mean that has “shrunk” towards the true population mean. Dozens of shrinkage estimators have been developed by various authors since Stein first introduced the idea in the 1950s. Popular ones include:

• Lasso estimator (used in lasso regression),
• Ridge estimator: used in ridge regression to improve the least-squares estimate when multicollinearity is present,
• Stein-type estimators, including the “original” James-Stein estimator.

Other shrinkage methods include step-wise regression, which reduces the shrinkage factor to zero or one, least angle regression and cross-validatory approaches.

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