Abstract: This article deals with the partially linear model y=X^τ_β+g(t)+ε, where ε~N(0,σ²), the predictor X is observable and the predictor t is measured with additive error. The nonparametric function g(t) is estimated by the method of the smoothing spline. The parameters are given the prior by according to the Bayesian explanation of the smoothing spline and Bayesian linear regression. The parametric posterior distribution is sampled by the method of Gibbs sampling. The parameters are estimated by the posterior mean and the parametric posterior interval can constructed by the quantile of samples drew from the posterior distribution. The simulated example is used to illustrate our methodology.

Key words: smoothing spline, regression of errors-in-variable, Bayesian method, Gibbs sampling, MCMC simulation, partially linear model, smoothing spline, regression of errors-in-variable, Bayesian method, Gibbs sampling, MCMC simulation