Quantile-slicing estimation for dimension reduction in regression

Hyungwoo Kim, Yichao Wu, Seung Jun Shin

Research output: Contribution to journalArticle

Abstract

Sufficient dimension reduction (SDR) has recently received much attention due to its promising performance under less stringent model assumptions. We propose a new class of SDR approaches based on slicing conditional quantiles: quantile-slicing mean estimation (QUME) and quantile-slicing variance estimation (QUVE). Quantile-slicing is particularly useful when the quantile function is more efficient to capture underlying model structure than the response itself, for example, when heteroscedasticity exists in a regression context. Both simulated and real data analysis results demonstrate promising performance of the proposed quantile-slicing SDR estimation methods.

Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalJournal of Statistical Planning and Inference
Volume198
DOIs
Publication statusPublished - 2019 Jan 1

Fingerprint

Slicing
Dimension Reduction
Quantile
Sufficient Dimension Reduction
Regression
Model structures
Conditional Quantiles
Quantile Function
Heteroscedasticity
Variance Estimation
Data analysis
Dimension reduction
Quantile estimation
Model
Demonstrate

Keywords

  • Heteroscedasticity
  • Kernel quantile regression
  • Quantile-slicing estimation
  • Sufficient dimension reduction

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Cite this

Quantile-slicing estimation for dimension reduction in regression. / Kim, Hyungwoo; Wu, Yichao; Shin, Seung Jun.

In: Journal of Statistical Planning and Inference, Vol. 198, 01.01.2019, p. 1-12.

Research output: Contribution to journalArticle

@article{581b4d4eb7c747b891ae5dce9e429c8e,
title = "Quantile-slicing estimation for dimension reduction in regression",
abstract = "Sufficient dimension reduction (SDR) has recently received much attention due to its promising performance under less stringent model assumptions. We propose a new class of SDR approaches based on slicing conditional quantiles: quantile-slicing mean estimation (QUME) and quantile-slicing variance estimation (QUVE). Quantile-slicing is particularly useful when the quantile function is more efficient to capture underlying model structure than the response itself, for example, when heteroscedasticity exists in a regression context. Both simulated and real data analysis results demonstrate promising performance of the proposed quantile-slicing SDR estimation methods.",
keywords = "Heteroscedasticity, Kernel quantile regression, Quantile-slicing estimation, Sufficient dimension reduction",
author = "Hyungwoo Kim and Yichao Wu and Shin, {Seung Jun}",
year = "2019",
month = "1",
day = "1",
doi = "10.1016/j.jspi.2018.03.001",
language = "English",
volume = "198",
pages = "1--12",
journal = "Journal of Statistical Planning and Inference",
issn = "0378-3758",
publisher = "Elsevier",

}

TY - JOUR

T1 - Quantile-slicing estimation for dimension reduction in regression

AU - Kim, Hyungwoo

AU - Wu, Yichao

AU - Shin, Seung Jun

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Sufficient dimension reduction (SDR) has recently received much attention due to its promising performance under less stringent model assumptions. We propose a new class of SDR approaches based on slicing conditional quantiles: quantile-slicing mean estimation (QUME) and quantile-slicing variance estimation (QUVE). Quantile-slicing is particularly useful when the quantile function is more efficient to capture underlying model structure than the response itself, for example, when heteroscedasticity exists in a regression context. Both simulated and real data analysis results demonstrate promising performance of the proposed quantile-slicing SDR estimation methods.

AB - Sufficient dimension reduction (SDR) has recently received much attention due to its promising performance under less stringent model assumptions. We propose a new class of SDR approaches based on slicing conditional quantiles: quantile-slicing mean estimation (QUME) and quantile-slicing variance estimation (QUVE). Quantile-slicing is particularly useful when the quantile function is more efficient to capture underlying model structure than the response itself, for example, when heteroscedasticity exists in a regression context. Both simulated and real data analysis results demonstrate promising performance of the proposed quantile-slicing SDR estimation methods.

KW - Heteroscedasticity

KW - Kernel quantile regression

KW - Quantile-slicing estimation

KW - Sufficient dimension reduction

UR - http://www.scopus.com/inward/record.url?scp=85044616983&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85044616983&partnerID=8YFLogxK

U2 - 10.1016/j.jspi.2018.03.001

DO - 10.1016/j.jspi.2018.03.001

M3 - Article

AN - SCOPUS:85044616983

VL - 198

SP - 1

EP - 12

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

ER -