Consistency of the Bayes Estimator of a Regression Curve

Published 19 Jul 2022 in math.ST and stat.TH | (2207.09573v1)

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.

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Agustin G. Nogales

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