Statistics and Its Interface

Volume 2 (2009)

Number 2

Bayesian R-estimates in linear models

Pages: 247 – 254



Thomas P. Hettmansperger (Department of Statistics, The Pennsylvania State University, University Park, Penn., U.S.A.)

Xiaojiang Zhan (Merck & Co., Inc., Rahway, New Jersey, U.S.A.)


A Beyesian approach to applying nonparametric rankbased methodology to linear models is discussed. Information in the data is summarized by a rank-based quantity, whose asymptotic distribution is used as a pseudolikelihood. The posterior distribution (up to a normalizing constant) of the coefficient(s) given the rank-based quantity can be obtained by assuming a prior distribution for the coefficient(s) in the linear model. This posterior distribution, together with simulation methods (typically the Markov Chain Monte Carlo methodology), can then be used for inference.


robust estimate, rank estimate, Bayesian analysis, linear models

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