Consistency of the Bayes Estimator of a Regression Curve

Abstract

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.

arXiv commentarXiv admin note: substantial text overlap with arXiv:2206.12379, arXiv:2110.13427