Asymptotically Optimal Regression Trees
(2018) In Working Papers- Abstract
- Regression trees are evaluated with respect to mean square error (MSE), mean integrated square error (MISE), and integrated squared error (ISE), as the size of the training sample goes to infinity. The asymptotically MSE- and MISE minimizing (locally adaptive) regression trees are characterized. Under an optimal tree, MSE is O(n^{-2/3}). The estimator is shown to be asymptotically normally distributed. An estimator for ISE is also proposed, which may be used as a complement to cross-validation in the pruning of trees.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/ddbfc5e8-172a-4391-9e5f-8e25b5818515
- author
- Mohlin, Erik LU
- organization
- publishing date
- 2018
- type
- Working paper/Preprint
- publication status
- published
- subject
- keywords
- Piece-Wise Linear Regression, Partitioning Estimators, Non-Parametric Regression, Categorization, Partition, Prediction Trees, Decision Trees, Regression Trees, Regressogram, Mean Squared Error, C14, C38
- in
- Working Papers
- issue
- 2018:12
- pages
- 27 pages
- language
- English
- LU publication?
- yes
- id
- ddbfc5e8-172a-4391-9e5f-8e25b5818515
- date added to LUP
- 2018-05-29 15:58:28
- date last changed
- 2024-09-10 00:21:22
@misc{ddbfc5e8-172a-4391-9e5f-8e25b5818515, abstract = {{Regression trees are evaluated with respect to mean square error (MSE), mean integrated square error (MISE), and integrated squared error (ISE), as the size of the training sample goes to infinity. The asymptotically MSE- and MISE minimizing (locally adaptive) regression trees are characterized. Under an optimal tree, MSE is O(n^{-2/3}). The estimator is shown to be asymptotically normally distributed. An estimator for ISE is also proposed, which may be used as a complement to cross-validation in the pruning of trees.}}, author = {{Mohlin, Erik}}, keywords = {{Piece-Wise Linear Regression; Partitioning Estimators; Non-Parametric Regression; Categorization; Partition; Prediction Trees; Decision Trees; Regression Trees; Regressogram; Mean Squared Error; C14; C38}}, language = {{eng}}, note = {{Working Paper}}, number = {{2018:12}}, series = {{Working Papers}}, title = {{Asymptotically Optimal Regression Trees}}, url = {{https://lup.lub.lu.se/search/files/194854013/WP18_12.pdf}}, year = {{2018}}, }