Bayesian curve estimation by model averaging

A Bayesian approach is used to estimate a nonparametric regression model. The main features of the procedure are, first, the functional form of the curve is approximated by a mixture of local polynomials by Bayesian model averaging (BMA), second, the model weights are approximated by the BIC criterion and third, a robust estimation procedure is incorporated to improve the smoothness of the estimated curve. The models considered at each sample points are polynomial regression models of order smaller than four, and the parameters are estimated by a local window. The predictive value is computed by BMA, and the posterior probability of each model is approximated by the exponential of the BIC criterion. Robustness is achieved by assuming that the noise follows a scale contaminated normal model, so that the effect of possible outliers is downweighted. The procedure provides a smooth curve and allows a straightforward prediction and quantification of the uncertainty. The method is illustrated with several examples and Monte Carlo experiments.