Abstract

This paper estimates an additive model semiparametrically, while automatically select-ing the significant independent variables and the app~opriatc power transformation of the dependent variable. The nonlinear variables arc modeled as regression splincs, with sig-nificant knots selected fiom a large number of candidate knots. The estimation is made robust by modeling the errors as a mixture of normals. A Bayesian approach is used to select the significant knots, the power transformation, and to identify oatliers using the Gibbs sampler to curry out the computation. Empirical evidence is given that the sampler works well on both simulated and real examples and that in the univariate case it compares faw)rably with a kernel-weighted local linear smoother, The variable selection algorithm in the paper is substantially fasler than previous Bayesian variable sclcclion algorithms. K('I ' word~': Additive nlodel, Pov¢¢r Iransformalio:l: Robust cslinlalion

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