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Bayesian Analysis of Composite Quantile Regression

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Abstract

This paper introduces a Bayesian approach for composite quantile regression employing the skewed Laplace distribution for the error distribution. We use a two-level hierarchical Bayesian model for coefficient estimation and future selection which assumes a prior distribution that favors sparseness. An efficient Gibbs sampling algorithm is developed to update the unknown quantities from the posteriors. The proposed approach is illustrated via simulation studies and two real datasets. Results indicate that the proposed approach performs quite good in comparison to the other approaches.

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Authors and Affiliations

  1. Statistics Department, College of Administration and Economics, Al-Qadisiyah University, Al Diwaniyah, Iraq

    Rahim Alhamzawi

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  1. Rahim Alhamzawi
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Correspondence to Rahim Alhamzawi.

Appendix

Appendix

A description of the Body dimensions dataset can be found on the Brq package: http://cran.r-project.org/web/packages/Brq/index.html. Here is a table listing briefly the dataset frame for 507 observations on 25 regressors including the outcome (weight).

y

Weight (kg)

\(x_1\)

Gender

\(x_2\)

Age (years)

\(x_3\)

Height (cm)

\(x_4\)

Biacromial diameter (cm)

\(x_5\)

Biiliac diameter, or “pelvic breadth” (cm)

\(x_6\)

Bitrochanteric diameter (cm)

\(x_7\)

Chest depth (cm)

\(x_8\)

Chest diameter (cm)

\(x_9\)

Elbow diameter (cm)

\(x_{10}\)

Wrist diameter (cm)

\(x_{11}\)

Knee diameter (cm)

\(x_{12}\)

Ankle diameter (cm)

\(x_{13}\)

Shoulder girth (cm)

\(x_{14}\)

Chest girth (cm)

\(x_{15}\)

Waist girth (cm)

\(x_{16}\)

Navel (or ”Abdominal”) girth

\(x_{17}\)

Hip girth (cm)

\(x_{18}\)

Thigh girth (cm)

\(x_{19}\)

Bicep girth (cm)

\(x_{20}\)

Forearm girth (cm)

\(x_{21}\)

Knee girth (cm)

\(x_{22}\)

Calf maximum girth (cm)

\(x_{23}\)

Ankle minimum girth (cm)

\(x_{24}\)

Wrist minimum girth (cm)

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Alhamzawi, R. Bayesian Analysis of Composite Quantile Regression. Stat Biosci 8, 358–373 (2016). https://doi.org/10.1007/s12561-016-9158-8

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  • DOI: https://doi.org/10.1007/s12561-016-9158-8

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