Estimation of linear composite quantile regression using EM algorithm

Tian, Yuzhu; Zhu, Qianqian; Tian, Maozai

doi:10.1016/j.spl.2016.05.019

Cited by 19 publications

(12 citation statements)

References 22 publications

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“…, Q, see Zou and Yuan (2008). Moreover, we can use redefined AIC or BIC criteria (Tian et al, 2016) to select Q as follows…”

Section: Standard Cqr Methodsmentioning

confidence: 99%

“…In this section, we first use Monte Carlo simulation studies to assess the finite sample performance of the proposed procedures and then demonstrate the application of the proposed methods with a real data analysis. Tian et al (2016) proposed redefined AIC and BIC to select number of composite quantiles Q. However, the performances of CQR method with different Q are very similar in their the simulation part.…”

Section: Numerical Studiesmentioning

confidence: 99%

“…Kai et al (2011) studied semiparametric CQR estimates for the semiparametric varying-coefficient partially linear model. For other references about CQR method see Tang et al (2012Tang et al ( , 2015, Jiang et al ( , 2013Jiang et al ( , 2014Jiang et al ( , 2015Jiang et al ( , 2016aJiang et al ( , 2016bJiang et al ( , 2018, Ning and Tang (2014), Zhang et al (2016), Tian et al (2016), and so on. These nice theoretical properties of CQR in linear regression motivate us to consider CQR method for massive datasets.…”

Section: Introductionmentioning

confidence: 99%

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Composite quantile regression for massive datasets

Jiang

et al. 2018

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Analysis of massive datasets is challenging owing to limitations of computer primary memory. Composite quantile regression (CQR) is a robust and efficient estimation method. In this paper, we extend CQR to massive datasets and propose a divide-and-conquer CQR method. The basic idea is to split the entire dataset into several blocks, applying the CQR method for data in each block, and finally combining these regression results via weighted average. The proposed approach significantly reduces the required amount of primary memory, and the resulting estimate will be as efficient as if the entire data set was analyzed simultaneously. Moreover, to improve the efficiency of CQR, we propose a weighted CQR estimation approach. To achieve sparsity with high-dimensional covariates, we develop a variable selection procedure to select significant parametric components and prove the method possessing the oracle property. Both simulations and data analysis are conducted to illustrate the finite sample performance of the proposed methods.

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“…, Q, see Zou and Yuan (2008). Moreover, we can use redefined AIC or BIC criteria (Tian et al, 2016) to select Q as follows…”

Section: Standard Cqr Methodsmentioning

confidence: 99%

Section: Numerical Studiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Composite quantile regression for massive datasets

Jiang

et al. 2018

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“…In this section we exploit Monte Carlo simulation to compare the finite sample performance of the DC-CQRNN method with CQRNN [18], QRNN [15,16], ANN [19], SVM [20], and RF [21]. e performances of the CQRNN method with different Q are very similar in the simulation of [22]. us, we only consider Q � 4, 9 as a compromise between the estimation and computational efficiency of the CQRNN method.…”

Section: Numerical Simulationsmentioning

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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“…To determine the number of components K is an important and challenging issue for mixture regression models, including the ALD mixture regression proposed. Tian et al (2016) studied the Algorithm 2 Composite quantile regression 1: Choose initial values β (0) and b (0) ; Let m = 0.…”

Section: Selection Of the Number Of Components Kmentioning

confidence: 99%