Bayesian quantile inference

The paper proposes a Bayesian interpretation of quantile regression that is shown to be equivalent to scale mixtures of normals leading to a skewed Laplace distribution. This representation of the model facilitates Bayesian analysis by means of Gibbs sampling with data augmentation, and nests regression in the L1 norm as a special case. The new methods are applied to an analysis of the patents - R&D relationship for U.S. firms and unit root inference for the dollar-deutschemark exchange rate.

[1]  K. Takeuchi,et al.  Second Order Asymptotic Bound for the Variance of Estimators for the Double Exponential Distribution , 2003 .

[2]  M. Steel,et al.  BAYESIAN REGRESSION ANALYSIS WITH SCALE MIXTURES OF NORMALS , 2000, Econometric Theory.

[3]  E. Tsionas.  Monte Carlo inference in econometric models with symmetric stable disturbances , 1999 .

[4]  Moshe Buchinsky.  Recent Advances in Quantile Regression Models: A Practical Guideline for Empirical Research , 1998 .

[5]  Martin L. Puterman,et al.  Analysis of Patent Data—A Mixed-Poisson-Regression-Model Approach , 1998 .

[6]  M. Steel,et al.  On Bayesian Modelling of Fat Tails and Skewness , 1998 .

[7]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

[8]  L. Tierney.  Markov Chains for Exploring Posterior Distributions , 1994 .

[9]  Adrian F. M. Smith,et al.  Simple conditions for the convergence of the Gibbs sampler and Metropolis-Hastings algorithms , 1994 .

[10]  J. Geweke,et al.  Bayesian Treatment of the Independent Student- t Linear Model , 1993 .

[11]  William Gould,et al.  Quantile regression with bootstrapped standard errors , 1993 .

[12]  H. V. Dijk,et al.  A Bayesian analysis of the unit root in real exchange rates , 1991 .

[13]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[14]  A. El-Shaarawi,et al.  ARMA Models with Double-exponentially Distributed Noise , 1989 .

[15]  Wesley M. Cohen,et al.  Empirical studies of innovation and market structure , 1989 .

[16]  May Thu Naing,et al.  Improved estimators for the location of double exponential distribution , 1989 .

[17]  Bronwyn H Hall,et al.  The R&D Master File Documentation , 1988 .

[18]  C. N. Morris,et al.  The calculation of posterior distributions by data augmentation , 1987 .

[19]  B. Efron.  Double Exponential Families and Their Use in Generalized Linear Regression , 1986 .

[20]  Roger Koenker,et al.  Tests of Linear Hypotheses and l[subscript]1 Estimation , 1982 .

[21]  R. Koenker,et al.  Robust Tests for Heteroscedasticity Based on Regression Quantiles , 1982 .

[22]  Roger Koenker,et al.  An empirical quantile function for linear models with iid errors , 1981 .

[23]  H. Harter,et al.  Adaptive Robust Estimation of Location and Scale Parameters of Symmetric Populations. , 1979 .

[24]  R. Koenker,et al.  Asymptotic Theory of Least Absolute Error Regression , 1978 .

[25]  D. F. Andrews,et al.  Robust Estimates of Location: Survey and Advances. , 1975 .

[26]  C. J. Lawrence.  Robust estimates of location : survey and advances , 1975 .