Sparse Composite Quantile Regression in Ultrahigh Dimensions With Tuning Parameter Calibration

Gu, Yuwen; Zou, Hui

doi:10.1109/tit.2020.3001090

Cited by 22 publications

(20 citation statements)

References 28 publications

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“…The derivation method in theory and algorithm of this paper can be well applied to more general model such as constrained Huber's estimation, quantile and composite quantile estimation (Gu and Zou 2020). For other penalty terms constrained regression such as elastic net, SCAD, MCP (Zhang 2010), the idea of nested ADMM is also available, but the theoretical analysis needs more technical methods.…”

Section: Discussionmentioning

confidence: 99%

“…The proof details of Lemma 4 can be found in the Appendix A. This cone constraint is extremely important for high dimensional estimation error bounds, one can see it in the classical lasso, square root lasso, LADlasso (quantile lasso) and constrained lasso, for example, Bickel et al (2009), Wang (2013), ), James et al (2013, Gu and Zou (2020). Now we introduce some restricted eigenvalue concepts on the design matrix X , based on L 2 norm to prepare for the analysis of near Oracle property of the pcLAD estimator.…”

Section: P Is High Dimensionalmentioning

confidence: 99%

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Penalized and constrained LAD estimation in fixed and high dimension

Ran

Yang

2021

Stat Papers

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Recently, many literatures have proved that prior information and structure in many application fields can be formulated as constraints on regression coefficients. Following these work, we propose a L 1 penalized LAD estimation with some linear constraints in this paper. Different from constrained lasso, our estimation performs well when heavy-tailed errors or outliers are found in the response. In theory, we show that the proposed estimation enjoys the Oracle property with adjusted normal variance when the dimension of the estimated coefficients p is fixed. And when p is much greater than the sample size n, the error bound of proposed estimation is sharper than k log( p)/n. It is worth noting the result is true for a wide range of noise distribution, even for the Cauchy distribution. In algorithm, we not only consider an typical linear programming to solve proposed estimation in fixed dimension , but also present an nested alternating direction method of multipliers (ADMM) in high dimension. Simulation and application to real data also confirm that proposed estimation is an effective alternative when constrained lasso is unreliable.

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Section: Discussionmentioning

confidence: 99%

Section: P Is High Dimensionalmentioning

confidence: 99%

Penalized and constrained LAD estimation in fixed and high dimension

Ran

Yang

2021

Stat Papers

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“…The two 2008 articles by Zou & Yuan study settings with a fixed number of parameters. Recently the composite quantile approach of Zou and Yuan (2008a) was extended to high dimensional scenarios by Gu and Zou (2020). These authors assume that the slopes are the same across quantiles, i.e.…”

Section: E{i(ymentioning

confidence: 99%

“…function considered in Zou and Yuan (2008a) and Gu and Zou (2020) is that we allow θ km = θ km (1 ≤ m = m ≤ M ; k = 1, . .…”

Section: Penalized Estimatormentioning

confidence: 99%

Data Integration in High Dimension With Multiple Quantiles

2023

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This article deals with the analysis of high dimensional data that come from multiple sources ("experiments") and thus have different possibly correlated responses, but share the same set of predictors. The measurements of the predictors may be different across experiments. We introduce a new regression approach with multiple quantiles to select those predictors that affect any of the responses at any quantile level and to estimate the nonzero parameters. Our approach differs from established methods by being able to handle heterogeneity in data sets as well as heavy-tailed error distributions, two difficulties that are often encountered in complex data scenarios. Our estimator is a minimizer of a penalized objective function, which aggregates the data from the different experiments. We establish model selection consistency and asymptotic normality of the estimator. In addition we present an information criterion, which can also be used for consistent model selection. Simulations and two data applications illustrate the advantages of our method in recovering the underlying regression models, which comes from taking the group structure induced by the predictors across experiments and quantile levels into account.

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“…Based on this method, a kind of composite quantile regressions (CQRs) (e.g. Zou and Yuan, 2008, Kai et al, 2010, Sun et al, 2013, Gu and Zou, 2020, Wang et al, 2021 have been proposed for parametric and nonparametric models. The CQRs enjoys great advantages in terms of estimation efficiency whether the variance of error is finite or not.…”

Section: Related Workmentioning

confidence: 99%

Global Bias-Corrected Divide-and-Conquer by Quantile-Matched Composite for General Nonparametric Regressions

Chen¹,

Li²

2022

Preprint

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The issues of bias-correction and robustness are crucial in the strategy of divide-andconquer (DC), especially for asymmetric nonparametric models with massive data. It is known that quantile-based methods can achieve the robustness, but the quantile estimation for nonparametric regression has non-ignorable bias when the error distribution is asymmetric. This paper explores a global bias-corrected DC by quantile-matched composite for nonparametric regressions with general error distributions. The proposed strategies can achieve the biascorrection and robustness, simultaneously. Unlike common DC quantile estimations that use

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Sparse Composite Quantile Regression in Ultrahigh Dimensions With Tuning Parameter Calibration

Cited by 22 publications

References 28 publications

Penalized and constrained LAD estimation in fixed and high dimension

Penalized and constrained LAD estimation in fixed and high dimension

Data Integration in High Dimension With Multiple Quantiles

Global Bias-Corrected Divide-and-Conquer by Quantile-Matched Composite for General Nonparametric Regressions

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