Consistency of the Bayes Estimator of a Regression Curve

2022/07/19 by Agustín García Nogales, Nogales, Agustin G.
Mathematics · Engineering · #Statistical Methods and Inference #Advanced Statistical Methods and Models #Reservoir Engineering and Simulation Methods

paper · pdf · doi:10.48550/arxiv.2207.09573

Abstract

Strong consistency of the Bayes estimator of a regression curve for the L¹-squared loss function is proved. It is also shown the convergence to 0 of the Bayes risk of this estimator both for the L¹ and L¹-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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