Composite quantile regression for massive datasets

Jiang, Rong; Hu, Xueping; Yu, Keming; Qian, Weimin

doi:10.1080/02331888.2018.1500579

Cited by 27 publications

(8 citation statements)

References 42 publications

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“…This is not surprising because the LAD estimator is just the minimizer of the MAE on the training set. This phenomenon is consistent with the results in real data example of Jiang et al (2018).…”

Section: Asymmetric Datasupporting

confidence: 93%

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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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Section: Asymmetric Datasupporting

confidence: 93%

“…However, this is a common condition in DC quantile methods with one-shot aggregation, even for parametric models, this condition is commonly used (see e.g. Zhao et al, 2015, Jiang et al, 2018, Chen and Zhou, 2020.…”

Section: Regularity Conditionsmentioning

confidence: 99%

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

Chen¹,

Li²

2022

Preprint

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“…where f(x i ) is an estimator of f(x i ). We employ EBIC in (7) to select L and λ, and the results are showed in Table 1. To reduce the computational load, we consider all the combinations of λ � 0, 0.05, .…”

Section: Prediction Performancementioning

confidence: 99%

“…A block average quantile regression (QR) approach for the massive dataset is proposed in [6] by combining the divide-and-conquer method with QR. Jiang [7] extended the work of [6] to composite quantile regression (CQR) for massive datasets. Recently, Chen et al [8] studied QR under memory constraint for massive datasets.…”

Section: Introductionmentioning

confidence: 99%

Composite Quantile Regression Neural Network for Massive Datasets

Jin

Zhao

2021

Mathematical Problems in Engineering

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Traditional statistical methods and machine learning on massive datasets are challenging owing to limitations of computer primary memory. Composite quantile regression neural network (CQRNN) is an efficient and robust estimation method. But most of existing computational algorithms cannot solve CQRNN for massive datasets reliably and efficiently. In this end, we propose a divide and conquer CQRNN (DC-CQRNN) method to extend CQRNN on massive datasets. The major idea is to divide the overall dataset into some subsets, applying the CQRNN for data within each subsets, and final results through combining these training results via weighted average. It is obvious that the demand for the amount of primary memory can be significantly reduced through our approach, and at the same time, the computational time is also significantly reduced. The Monte Carlo simulation studies and an environmental dataset application verify and illustrate that our proposed approach performs well for CQRNN on massive datasets. The environmental dataset has millions of observations. The proposed DC-CQRNN method has been implemented by Python on Spark system, and it takes 8 minutes to complete the model training, whereas a full dataset CQRNN takes 5.27 hours to get a result.

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“…We denote this algorithm as EIS Q . Second, we propose three efficient importance sampling imputation algorithms in composite quantile regression (denoted as EIS CQ ) using IP, majorize‐minimization (MM) and coordinate descent (CD) based on publicly available cqrReg package for R [4, 8, 9, 21]. For brevity, we denote the above three EIS algorithms in composite quantile regression as

{normalEIS}_{italicCQ}^{normalIP}

{normalEIS}_{italicCQ}^{normalMM}

and

{normalEIS}_{italicCQ}^{normalCD}

, respectively.…”

Section: Introductionmentioning

confidence: 99%

Efficient importance sampling imputation algorithms for quantile and composite quantile regression

Cheng

2021

Statistical Analysis

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Nowadays, missing data in regression model is one of the most well‐known topics. In this paper, we propose a class of efficient importance sampling imputation algorithms (EIS) for quantile and composite quantile regression with missing covariates. They are an EIS in quantile regression (EISQ) and its three extensions in composite quantile regression (EISCQ). Our EISQ uses an interior point (IP) approach, while EISCQ algorithms use IP and other two well‐known approaches: Majorize‐minimization (MM) and coordinate descent (CD). The aims of our proposed EIS algorithms are to decrease estimated variances and relieve computational burden at the same time, which improves the performances of coefficients estimators in both estimated and computational efficiencies. To compare our EIS algorithms with other existing competitors including complete cases analysis and multiple imputation, the paper carries out a series of simulation studies with different sample sizes and different levels of missing rates under different missing mechanism models. Finally, we apply all the algorithms to part of the examination data in National Health and Nutrition Examination Survey.

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Composite quantile regression for massive datasets

Cited by 27 publications

References 42 publications

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

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

Composite Quantile Regression Neural Network for Massive Datasets

Efficient importance sampling imputation algorithms for quantile and composite quantile regression

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