PRESS statistic
In statistics, the predicted residual error sum of squares (PRESS) is a form of cross-validation used in regression analysis to provide a summary measure of the fit of a model to a sample of observations that were not themselves used to estimate the model. It is calculated as the sums of squares of the prediction residuals for those observations.[1][2][3]
A fitted model having been produced, each observation in turn is removed and the model is refitted using the remaining observations. The out-of-sample predicted value is calculated for the omitted observation in each case, and the PRESS statistic is calculated as the sum of the squares of all the resulting prediction errors:[4]
- [math]\displaystyle{ \operatorname{PRESS} =\sum_{i=1}^n (y_i - \hat{y}_{i, -i})^2 }[/math]
Given this procedure, the PRESS statistic can be calculated for a number of candidate model structures for the same dataset, with the lowest values of PRESS indicating the best structures. Models that are over-parameterised (over-fitted) would tend to give small residuals for observations included in the model-fitting but large residuals for observations that are excluded. PRESS statistic has been extensively used in Lazy Learning and locally linear learning to speed-up the assessment and the selection of the neighbourhood size.[5][6]
See also
References
- ↑ "Statsoft Electronic Statistics Textbook - Statistics Glossary". http://www.statsoft.com/textbook/statistics-glossary/p#PRESS%20Statistic. Retrieved May 13, 2016.
- ↑ Allen, D. M. (1974), "The Relationship Between Variable Selection and Data Augmentation and a Method for Prediction," Technometrics, 16, 125–127
- ↑ Tarpey, Thaddeus (2000) "A Note on the Prediction Sum of Squares Statistic for Restricted Least Squares", The American Statistician, Vol. 54, No. 2, May, pp. 116–118
- ↑ "R Graphical Manual:Allen's PRESS (Prediction Sum-Of-Squares) statistic, aka P-square". https://www.rdocumentation.org/packages/qpcR/versions/1.4-0/topics/PRESS. Retrieved February 27, 2018.
- ↑ Atkeson, Christopher G.; Moore, Andrew W.; Schaal, Stefan (1 February 1997). "Locally Weighted Learning" (in en). Artificial Intelligence Review 11 (1): 11–73. doi:10.1023/A:1006559212014. ISSN 1573-7462. https://link.springer.com/article/10.1023/A:1006559212014. Retrieved 25 September 2020.
- ↑ Bontempi, Gianluca; Birattari, Mauro; Bersini, Hugues (1 January 1999). "Lazy learning for local modelling and control design". International Journal of Control 72 (7–8): 643–658. doi:10.1080/002071799220830.
 |  |
