• Title, Summary, Keyword: penalized quantile regression

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Quantile Regression with Non-Convex Penalty on High-Dimensions

  • Choi, Ho-Sik;Kim, Yong-Dai;Han, Sang-Tae;Kang, Hyun-Cheol
    • Communications for Statistical Applications and Methods
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    • v.16 no.1
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    • pp.209-215
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    • 2009
  • In regression problem, the SCAD estimator proposed by Fan and Li (2001), has many desirable property such as continuity, sparsity and unbiasedness. In this paper, we extend SCAD penalized regression framework to quantile regression and hence, we propose new SCAD penalized quantile estimator on high-dimensions and also present an efficient algorithm. From the simulation and real data set, the proposed estimator performs better than quantile regression estimator with $L_1$ norm.

Two-Stage Penalized Composite Quantile Regression with Grouped Variables

  • Bang, Sungwan;Jhun, Myoungshic
    • Communications for Statistical Applications and Methods
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    • v.20 no.4
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    • pp.259-270
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    • 2013
  • This paper considers a penalized composite quantile regression (CQR) that performs a variable selection in the linear model with grouped variables. An adaptive sup-norm penalized CQR (ASCQR) is proposed to select variables in a grouped manner; in addition, the consistency and oracle property of the resulting estimator are also derived under some regularity conditions. To improve the efficiency of estimation and variable selection, this paper suggests the two-stage penalized CQR (TSCQR), which uses the ASCQR to select relevant groups in the first stage and the adaptive lasso penalized CQR to select important variables in the second stage. Simulation studies are conducted to illustrate the finite sample performance of the proposed methods.

Penalized quantile regression tree (벌점화 분위수 회귀나무모형에 대한 연구)

  • Kim, Jaeoh;Cho, HyungJun;Bang, Sungwan
    • The Korean Journal of Applied Statistics
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    • v.29 no.7
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    • pp.1361-1371
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    • 2016
  • Quantile regression provides a variety of useful statistical information to examine how covariates influence the conditional quantile functions of a response variable. However, traditional quantile regression (which assume a linear model) is not appropriate when the relationship between the response and the covariates is a nonlinear. It is also necessary to conduct variable selection for high dimensional data or strongly correlated covariates. In this paper, we propose a penalized quantile regression tree model. The split rule of the proposed method is based on residual analysis, which has a negligible bias to select a split variable and reasonable computational cost. A simulation study and real data analysis are presented to demonstrate the satisfactory performance and usefulness of the proposed method.

Quantile regression using asymmetric Laplace distribution (비대칭 라플라스 분포를 이용한 분위수 회귀)

  • Park, Hye-Jung
    • Journal of the Korean Data and Information Science Society
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    • v.20 no.6
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    • pp.1093-1101
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    • 2009
  • Quantile regression has become a more widely used technique to describe the distribution of a response variable given a set of explanatory variables. This paper proposes a novel modelfor quantile regression using doubly penalized kernel machine with support vector machine iteratively reweighted least squares (SVM-IRWLS). To make inference about the shape of a population distribution, the widely popularregression, would be inadequate, if the distribution is not approximately Gaussian. We present a likelihood-based approach to the estimation of the regression quantiles that uses the asymmetric Laplace density.

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A numerical study on group quantile regression models

  • Kim, Doyoen;Jung, Yoonsuh
    • Communications for Statistical Applications and Methods
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    • v.26 no.4
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    • pp.359-370
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    • 2019
  • Grouping structures in covariates are often ignored in regression models. Recent statistical developments considering grouping structure shows clear advantages; however, reflecting the grouping structure on the quantile regression model has been relatively rare in the literature. Treating the grouping structure is usually conducted by employing a group penalty. In this work, we explore the idea of group penalty to the quantile regression models. The grouping structure is assumed to be known, which is commonly true for some cases. For example, group of dummy variables transformed from one categorical variable can be regarded as one group of covariates. We examine the group quantile regression models via two real data analyses and simulation studies that reveal the beneficial performance of group quantile regression models to the non-group version methods if there exists grouping structures among variables.

Support vector quantile regression ensemble with bagging

  • Shim, Jooyong;Hwang, Changha
    • Journal of the Korean Data and Information Science Society
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    • v.25 no.3
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    • pp.677-684
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    • 2014
  • Support vector quantile regression (SVQR) is capable of providing more complete description of the linear and nonlinear relationships among random variables. To improve the estimation performance of SVQR we propose to use SVQR ensemble with bagging (bootstrap aggregating), in which SVQRs are trained independently using the training data sets sampled randomly via a bootstrap method. Then, they are aggregated to obtain the estimator of the quantile regression function using the penalized objective function composed of check functions. Experimental results are then presented, which illustrate the performance of SVQR ensemble with bagging.