PRESS statistic
Today, the topic of PRESS statistic is of great relevance and interest to a wide spectrum of society. From its impact on the economy to its influence on people's daily lives, PRESS statistic has generated debate and reflection in various areas. As we move into the 21st century, we cannot ignore the importance of PRESS statistic and its complex relationship with other aspects of modern life. In this article we will explore different perspectives and approaches on PRESS statistic, analyzing its meaning, implications and possible challenges. Through detailed analysis, we hope to discover new ideas and perspectives that will help us better understand the role PRESS statistic plays in our world today.
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.
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:
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.
See also
References
- ^ "Statsoft Electronic Statistics Textbook - Statistics Glossary". Archived from the original on May 10, 2016. 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". Archived from the original on February 27, 2018. Retrieved February 27, 2018.
- ^ Atkeson, Christopher G.; Moore, Andrew W.; Schaal, Stefan (1 February 1997). "Locally Weighted Learning". Artificial Intelligence Review. 11 (1): 11–73. doi:10.1023/A:1006559212014. ISSN 1573-7462. S2CID 9219592. Archived from the original on 6 May 2021. 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.
 | This statistics-related article is a stub. You can help Wikipedia by expanding it. |