Consistency of the Bayes Estimator of a Regression Curve
Strong consistency of the Bayes estimator of a regression curve for the L^1-squared loss function is proved. It is also shown the convergence to 0 of the Bayes risk of this estimator both for the L^1 and L^1-squared loss functions. The Bayes estimator of a regression curve is the regression curve with respect to the posterior predictive distribution.
READ FULL TEXT