Single-index composite quantile regression for massive data

Jiang, Rong; Yu, Keming

doi:10.1016/j.jmva.2020.104669

Cited by 10 publications

(5 citation statements)

References 38 publications

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“…We denote the target function in (11) by Q S * λ (a, b, γ). We can easily discover that Q S * λ is invariant, so when minimizing Q S * λ , we restrict γ = 1 to be the unit length γ = 1 through normalization γ.…”

Section: Computationmentioning

confidence: 99%

“…[3] proposed D-Vine Copula-based quantile regression, which is a new algorithm that does not require accurately assuming the shape of conditional quantiles and avoids the typical defects of linear models, such as multicollinearity. [11] proposed a non-iterative coincidence quantile regression (NICQR) estimation algorithm for the singleindex quantile regression model, which has high computational efficiency and is suitable for analyzing massive data sets.…”

Section: Introductionmentioning

confidence: 99%

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Robust Variable Selection Based on Penalized Composite Quantile Regression for High-Dimensional Single-Index Models

Song

Fang

2022

Mathematics

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The single-index model is an intuitive extension of the linear regression model. It has been increasingly popular due to its flexibility in modeling. In this work, we focus on the estimators of the parameters and the unknown link function for the single-index model in a high-dimensional situation. The SCAD and Laplace error penalty (LEP)-based penalized composite quantile regression estimators, which could realize variable selection and estimation simultaneously, are proposed; a practical iterative algorithm is introduced to obtain the efficient and robust estimators. The choices of the tuning parameters, the bandwidth, and the initial values are also discussed. Furthermore, under some mild conditions, we show the large sample properties and oracle property of the SCAD and Laplace penalized composite quantile regression estimators. Finally, we evaluated the performances of the proposed estimators by two numerical simulations and a real data application.

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Section: Computationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust Variable Selection Based on Penalized Composite Quantile Regression for High-Dimensional Single-Index Models

Song

Fang

2022

Mathematics

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“…Liu et al [ 15 ]considered weighted composite quantile estimation of the single-index model with missing covariates at random. Jiang and Yu [ 16 ] extended the non-iterative composite quantile regression methods for single-index models to the analysis of massive datasets via a divide-and-conquer strategy. The proposed approach significantly reduced the computing time and the required primary memory.…”

Section: Introductionmentioning

confidence: 99%

Bayesian composite quantile regression for the single-index model

Yuan

Xiang

2023

PLoS ONE

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By using a Gaussian process prior and a location-scale mixture representation of the asymmetric Laplace distribution, we develop a Bayesian analysis for the composite quantile single-index regression model. The posterior distributions for the unknown parameters are derived, and the Markov chain Monte Carlo sampling algorithms are also given. The proposed method is illustrated by three simulation examples and a real dataset.

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“…The single-index model has the following advantages: (i) the single-index in the link function projects multivariate covariates onto a one-dimensional variate, which effectively overcomes the "curse of dimensionality"; (ii) the unspecified link function allows model flexibility and thus has a lower risk of misspecification; and (iii) the interpretation of covariate effects is easy because of the linear structure of the index. Therefore, single-index quantile regression (1.1) has received extensive attention in the literature in the recent years; see Chaudhuri et al (1997), Wu et al (2010), Oh et al (2011), Kong and Xia (2012), Lv et al (2015), Christou and Akritas (2016), Jiang et al (2016), Ma and He (2016), Tang et al (2018), Jiang and Yu (2020), and among others.…”

Section: Introductionmentioning

confidence: 99%

No-Crossing Single-Index Quantile Regression Curve Estimation

Jiang

2022

Journal of Business & Economic Statistics

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Single-index quantile regression (QR) models can avoid the curse of dimensionality in nonparametric problems by assuming that the response is only related to a single linear combination of the covariates. Like the standard parametric or nonparametric QR whose estimated curves may cross, the single-index QR can also suffer quantile crossing, leading to an invalid distribution for the response. This issue has attracted considerable attention in the literature in the recent year. In this article, we consider single-index models, develop methods for QR that guarantee noncrossing quantile curves, and extend the methods and results to composite quantile regression. The asymptotic properties of the proposed estimators are derived and their advantages over existing methods are explained. Simulation studies and a real data application are conducted to illustrate the finite sample performance of the proposed methods.

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Single-index composite quantile regression for massive data

Cited by 10 publications

References 38 publications

Robust Variable Selection Based on Penalized Composite Quantile Regression for High-Dimensional Single-Index Models

Robust Variable Selection Based on Penalized Composite Quantile Regression for High-Dimensional Single-Index Models

Bayesian composite quantile regression for the single-index model

No-Crossing Single-Index Quantile Regression Curve Estimation

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