Consistency of the Bayes Estimator of a Regression Curve

07/19/2022

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by   Agustin G. Nogales, et al.

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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.