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Asymptotically Optimal Regression Trees

Mohlin, Erik LU (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.
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author
organization
publishing date
type
Working Paper
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
alternative location
https://swopec.hhs.se/lunewp/abs/lunewp2018_012.htm
date added to LUP
2018-05-29 15:58:28
date last changed
2018-11-21 21:40:05
@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},
  keyword      = {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},
  pages        = {27},
  series       = {Working Papers },
  title        = {Asymptotically Optimal Regression Trees},
  year         = {2018},
}