Consistency of the Bayes Estimator of a Regression Curve

Agustin G. Nogales

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arXiv · 2207.09573

Consistency of the Bayes Estimator of a Regression Curve

Agustin G. Nogales

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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. 2022-07-19. Consistency of the Bayes Estimator of a Regression Curve. https://arxiv.org/abs/2207.09573

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