Bayesian variable selection and estimation in maximum entropy quantile regression

Tu, Shiyi; Wang, Min; Sun, Xiaoduan

doi:10.1080/02664763.2016.1168369

Cited by 11 publications

(4 citation statements)

References 24 publications

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“…us, the asymmetric Laplace distribution (ALD) is generally specified as the likelihood of the model. Tu et al [14] mentioned that the ALD has several mixture representations, for example, a scale mixture of normal with exponential distribution (2015) and a scale mixture of uniform with Gamma distribution according to Wichitaksorn et al [15]. In this study, we consider the ALD as a mixture of normal as it was proved to be more efficient than as a scale mixture of uniform.…”

Section: Copula-based Seemingly Unrelated Quantile Regression Modelmentioning

confidence: 96%

Bayesian Estimation of Archimedean Copula-Based SUR Quantile Models

2020

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We propose a high-dimensional copula to model the dependence structure of the seemingly unrelated quantile regression. As the conventional model faces with the strong assumption of the multivariate normal distribution and the linear dependence structure, thus, we apply the multivariate exchangeable copula function to relax this assumption. As there are many parameters to be estimated, we consider the Bayesian Markov chain Monte Carlo approach to estimate the parameter interests in the model. Four simulation studies are conducted to assess the performance of our proposed model and Bayesian estimation. Satisfactory results from simulation studies are obtained suggesting the good performance and reliability of the Bayesian method used in our proposed model. The real data analysis is also provided, and the empirical comparison indicates our proposed model outperforms the conventional models in all considered quantile levels.

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Section: Copula-based Seemingly Unrelated Quantile Regression Modelmentioning

confidence: 96%

Bayesian Estimation of Archimedean Copula-Based SUR Quantile Models

2020

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“…First, it offers more valuable information on the predictors' effects on different response variable quantifications than the regular mean regression. Second, it is relatively insensitive to heteroscedasticity, outliers, or other anomalies of latent responses, and thus, the quantile regression can accommodate non-normal errors commonly encountered in many practical applications [13][14][15]. Those two strengths resulted in a rapid expansion of the quantile regression application over recent years, particularly in social sciences, public health, medicine, and econometrics.…”

Section: Introductionmentioning

confidence: 99%

Modified Quantile Regression for Modeling the Low Birth Weight

Yanuar

Yozza

Zetra

2022

Front. Appl. Math. Stat.

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This study aims to identify the best model of low birth weight by applying and comparing several methods based on the quantile regression method's modification. The birth weight data is violated with linear model assumptions; thus, quantile approaches are used. The quantile regression is adjusted by combining it with the Bayesian approach since the Bayesian method can produce the best model in small size samples. Three kinds of the modified quantile regression methods considered here are the Bayesian quantile regression, the Bayesian Lasso quantile regression, and the Bayesian Adaptive Lasso quantile regression. This article implements the skewed Laplace distribution as the likelihood function in Bayesian analysis. The cross-sectional study collected the primary data of 150 birth weights in West Sumatera, Indonesia. This study indicated that Bayesian Adaptive Lasso quantile regression performed well compared to the other two methods based on a smaller absolute bias and a shorter Bayesian credible interval based on the simulation study. This study also found that the best model of birth weight is significantly affected by maternal education, the number of pregnancy problems, and parity.

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“…Here we take a different tack, and build on the statistical perspective developed in [1] to develop a simple modification of the PLQ estimation problem to infer shape parameters simultaneously with variables of interest. The most relevant works related to this paper focus on the relation between the quantile penalty and the asymmetric Laplace distribution(ALD) [8,30,33]. In particular, [8] jointly estimate the model and the shape parameters for quantile penalty, and [30] infer the joint posterior distribution of these parameters.…”

Section: −κ κmentioning

confidence: 99%

“…The most relevant works related to this paper focus on the relation between the quantile penalty and the asymmetric Laplace distribution(ALD) [8,30,33]. In particular, [8] jointly estimate the model and the shape parameters for quantile penalty, and [30] infer the joint posterior distribution of these parameters.…”

Section: −κ κmentioning

confidence: 99%

Estimating Shape Parameters of Piecewise Linear-Quadratic Problems

Zheng¹,

Ramamurthy²,

Aravkin³

2021

Open Journal of Mathematical Optimization

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Piecewise Linear-Quadratic (PLQ) penalties are widely used to develop models in statistical inference, signal processing, and machine learning. Common examples of PLQ penalties include least squares, Huber, Vapnik, 1-norm, and their asymmetric generalizations. Properties of these estimators depend on the choice of penalty and its shape parameters, such as degree of asymmetry for the quantile loss, and transition point between linear and quadratic pieces for the Huber function.In this paper, we develop a statistical framework that can help the modeler to automatically tune shape parameters once the shape of the penalty has been chosen. The choice of the parameter is informed by the basic notion that each PLQ penalty should correspond to a true statistical density. The normalization constant inherent in this requirement helps to inform the optimization over shape parameters, giving a joint optimization problem over these as well as primary parameters of interest. A second contribution is to consider optimization methods for these joint problems. We show that basic first-order methods can be immediately brought to bear, and design specialized extensions of interior point (IP) methods for PLQ problems that can quickly and efficiently solve the joint problem. Synthetic problems and larger-scale practical examples illustrate the utility of the approach. Code for the new IP method is implemented using the Julia language (https://github.com/UW-AMO/shape-parameters/tree/ojmo).

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Bayesian variable selection and estimation in maximum entropy quantile regression

Cited by 11 publications

References 24 publications

Bayesian Estimation of Archimedean Copula-Based SUR Quantile Models

Bayesian Estimation of Archimedean Copula-Based SUR Quantile Models

Modified Quantile Regression for Modeling the Low Birth Weight

Estimating Shape Parameters of Piecewise Linear-Quadratic Problems

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