Confidence sets for split points in decision trees
By Moulinath Banerjee, Ian W. McKeague. 2007
72 citations recorded by the source corpus.
B¨ uhlmann and Yu (2002) recently found the limiting distribution of the least squares estimator of split points in decision trees (CART). Their result is an instance of cube-root asymptotics with a non-normal limit, and raises the interesting question of how to construct confidence sets for split points. The bootstrap fails in this setting, and standard (Wald type) confidence intervals are found to be inaccurate. The present paper introduces a confidence set constructed by inverting a centered residual sum of squares statistic. A motivation for developing such a confidence set comes from the problem of phosphorus pollution in the Everglades. Ecologists have suggested that split points provide a phosphorus threshold at which biological imbalance occurs, and the lower endpoint of the confidence set may be interpreted as a level that is protective of the ecosystem. This is illustrated using data from a Duke University Wetlands Center phosphorus dosing study in the Everglades.
Subfields: Artificial Intelligence, Environmental Chemistry, Statistics and Probability
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Gérard Biau
- Erwan Scornet
- Giles Hooker
- Bodhisattva Sen
- Cécile Durot
- Yichen Zhou
- Stefan Wager
- Moulinath Banerjee
In Environmental Chemistry
In Statistics and Probability
- Cécile Durot
- Bodhisattva Sen
- Gérard Biau
- Erwan Scornet
- Giles Hooker
- Moulinath Banerjee
- Yichen Zhou
- Adityanand Guntuboyina
Citations in the corpus
- Interpreting Models via Single Tree Approximation (2016, background): “A theoretical discussion of the evaluation of splits can be found in Banerjee et al. [2007].”
- Divide and conquer in nonstandard problems and the super-efficiency phenomenon (2016, methodology): “, estimation of the mode [9], Manski’s maximum score estimator [21], change-point estimation under smooth mis-specification [4], least absolute median of squares [26], shorth estimation [13].”
- A random forest guided tour (2015, methodology): “Interestingly, Banerjee and McKeague (2007) refer to the study of Qian et al. (2003) on the effects of phosphorus pollution in the Everglades, which uses split points in a novel way.”