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Bayesian quantile regression. (English) Zbl 0983.62017
Summary: The paper introduces the idea of Bayesian quantile regression employing a likelihood function that is based on the asymmetric Laplace distribution. It is shown that irrespective of the original distribution of the data, the use of the asymmetric Laplace distribution is a very natural and effective way for modelling Bayesian quantile regression. The paper also demonstrates that improper uniform priors for the unknown model parameters yield a proper joint posterior. The approach is illustrated via a simulated and two real data sets.

62F15 Bayesian inference
62J05 Linear regression; mixed models
65C60 Computational problems in statistics (MSC2010)
bayesQR; R; S-PLUS
Full Text: DOI
[1] Buchinsky, M., Recent advances in quantile regression models, J. hum. res., 33, 88-126, (1998)
[2] Cole, T.J.; Green, P.J., Smoothing reference centile curves: LMS method and penalized likelihood, Statist. medic., 11, 1305-1319, (1992)
[3] Fatti, L.P.; Senaoana, E.M., Bayesian updating in reference centile charts, J. R. statist. soc. A, 161, 103-115, (1998)
[4] Gilks, W.R.; Richardson, S.; Spiegelhalter, D.J., Introducing Markov chain Monte Carlo., (), 1-19 · Zbl 0845.60072
[5] He, X.; Ng, P.; Portnoy, S., Bivaraite quantile smoothing splines, J. R. statist. soc. B, 60, 537-550, (1998) · Zbl 0909.62038
[6] Huber, P.J., Robust statistics., (1981), Wiley New York
[7] Isaacs, D.; Altman, D.G.; Tidmarsh, C.E.; Valman, H.B.; Webster, A.D.B., Serum immunoglobin concentrations in preschool children measured by laser nephelometry: reference ranges for igg, iga, igm, J. clin. pathol., 36, 1193-1196, (1983)
[8] Koenker, R.; Bassett, G.S., Regression quantiles, Econometrica, 46, 33-50, (1978) · Zbl 0373.62038
[9] Koenker, R.; Machado, J., Goodness of fit and related inference processes for quantile regression, J. amer. statist. assoc., 94, 1296-1309, (1999) · Zbl 0998.62041
[10] Royston, P.; Altman, D.G., Regression using fractional polynomials of continuous covariates: parsimonious parametric modelling (with discussion), Appl. statist., 43, 429-467, (1994)
[11] Venables, W.N.; Ripley, B.D., Modern applied statistics with S-PLUS, (2000), Springer New York · Zbl 0999.62502
[12] Yu, K.; Jones, M.C., Local linear regression quantile estimation, J. amer. statist. assoc., 93, 228-238, (1998) · Zbl 0906.62038
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