Skip to content
DraconiticResearch
Search Sources API
189,280 studies31 sourcesUpdated 38 min ago
Peer-reviewedCC BY 4.0Mathematics

CART Leaf Summaries via Bootstrap Bias Correction

  • George Ekow Quaye1
  • John Koomson2
  • Kwesi Appau Ohene-Obeng3
  • Xiaogang Su3
  1. 1Biostatistics and Computational Biology Core, Center for Population Health and Outcomes Research, Children’s Mercy Kansas City, Kansas City, MO 64108, USA
  2. 2Department of Mathematical Sciences, Central Connecticut State University, New Britain, CT 06050, USA
  3. 3Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, USA
Open at sourceDOICite

Abstract

CART provides interpretable tree models, but its data-adaptive construction can distort inference for terminal-node summaries. Comparing fitted trees with large independent reference samples, we find that regression terminal-node means are generally well calibrated, whereas standard deviations tend to be underestimated; in binary classification, terminal-node class proportions are often overly extreme, leading to downward-biased Bernoulli variance estimates. We propose a bootstrap bias correction (BBC) procedure that accounts for variation in tree structure by matching bootstrap-tree nodes to those of the original tree using observation overlap. Across simulations, BBC reduces error in regression standard deviations under nonlinear signal structures and improves class-probability and variance estimation in classification. Its benefits diminish, and it may slightly overcorrect, when the true tree structure is recovered nearly perfectly and uncorrected error is already small. Applications to Major League Baseball salary and Pima diabetes data illustrate BBC as a practical approach for mitigating adaptive distortion in CART terminal-node estimation.

Related

  1. Reference-State Bootstrap Correction and Kernel Characterization of Residual-Based Fit Indices in Structural Equation Models
    Eunjeong Song, Sehee Hong
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  2. On multiplicative bias correction in kernel density estimation
    M. C. Jones, D. F. Signorini, Nils Lid Hjort
    Open Research Online - ORO (The Open University)PreprintLicence not statedFull text16 citedStatisticsOpenAlex
  3. Bias Correction and Inference for Panel Quantile Regression
    Harold D Chiang, Wei Biao Wu
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  4. Inference for conditional Fréchet means via Riemannian Robust Bias Correction
    Ryunosuke Miyazaki, Chang Jun Im
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  5. Nonparametric covariance estimation with bias correction for spatial lattice processes
    Antonio Fioravanti, Carsten Jentsch
    arXivPreprintarXiv licenceFull textStatisticsarXiv

Cite

BibTeXRIS
BibTeX
@article{quaye2026cart,
  title = {{CART Leaf Summaries via Bootstrap Bias Correction}},
  author = {George Ekow Quaye and John Koomson and Kwesi Appau Ohene-Obeng and Xiaogang Su},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14213891},
  url = {https://www.mdpi.com/2227-7390/14/21/3891},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - CART Leaf Summaries via Bootstrap Bias Correction
AU  - George Ekow Quaye
AU  - John Koomson
AU  - Kwesi Appau Ohene-Obeng
AU  - Xiaogang Su
PY  - 2026
DA  - 2026/10/25
JO  - Mathematics
DO  - 10.3390/math14213891
UR  - https://www.mdpi.com/2227-7390/14/21/3891
AB  - CART provides interpretable tree models, but its data-adaptive construction can distort inference for terminal-node summaries. Comparing fitted trees with large independent reference samples, we find that regression terminal-node means are generally well calibrated, whereas standard deviations tend to be underestimated; in binary classification, terminal-node class proportions are often overly extreme, leading to downward-biased Bernoulli variance estimates. We propose a bootstrap bias correction (BBC) procedure that accounts for variation in tree structure by matching bootstrap-tree nodes to those of the original tree using observation overlap. Across simulations, BBC reduces error in regression standard deviations under nonlinear signal structures and improves class-probability and variance estimation in classification. Its benefits diminish, and it may slightly overcorrect, when the true tree structure is recovered nearly perfectly and uncorrected error is already small. Applications to Major League Baseball salary and Pima diabetes data illustrate BBC as a practical approach for mitigating adaptive distortion in CART terminal-node estimation.
SN  - 2227-7390
ER  -