Multiple quantile modeling via reduced-rank regression

Heng Lian, Weihua Zhao, Yanyuan Ma

Research output: Contribution to journalArticle

Abstract

Quantile regression estimators at a fixed quantile level rely mainly on a small subset of the observed data. As a result, efforts have been made to construct simultaneous estimations at multiple quantile levels in order to take full advantage of all observations and to improve the estimation efficiency. We propose a novel approach that links multiple linear quantile models by imposing a condition on the rank of the matrix formed by all of the regression parameters. This approach resembles a reduced-rank regression, but also shares similarities with the dimension-reduction modeling. We develop estimation and inference tools for such models and examine their optimality in terms of the asymptotic estimation variance. We use simulation experiments to examine the numerical performance of the proposed procedure, and a data example to further illustrate the method.

Original languageEnglish (US)
Pages (from-to)1439-1464
Number of pages26
JournalStatistica Sinica
Volume29
Issue number3
DOIs
StatePublished - Jan 1 2019

Fingerprint

Reduced Rank Regression
Quantile
Modeling
Simultaneous Estimation
Quantile Regression
Variance Estimation
Regression Estimator
Dimension Reduction
Simulation Experiment
Optimality
Regression
Subset
Model
Reduced rank regression

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Lian, Heng ; Zhao, Weihua ; Ma, Yanyuan. / Multiple quantile modeling via reduced-rank regression. In: Statistica Sinica. 2019 ; Vol. 29, No. 3. pp. 1439-1464.
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Multiple quantile modeling via reduced-rank regression. / Lian, Heng; Zhao, Weihua; Ma, Yanyuan.

In: Statistica Sinica, Vol. 29, No. 3, 01.01.2019, p. 1439-1464.

Research output: Contribution to journalArticle

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