Optimal Bayesian Estimation of a Regression Curve, a Conditional Density, and a Conditional Distribution

Agustín G. Nogales
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Agustín G. Nogales: Departamento de Matemáticas, IMUEx, Universidad de Extremadura, 06006 Badajoz, Spain

Mathematics, 2022, vol. 10, issue 8, 1-22

Abstract: In this paper, several related estimation problems are addressed from a Bayesian point of view, and optimal estimators are obtained for each of them when some natural loss functions are considered. The problems considered are the estimation of a regression curve, a conditional distribution function, a conditional density, and even the conditional distribution itself. These problems are posed in a sufficiently general framework to cover continuous and discrete, univariate and multivariate, and parametric and nonparametric cases, without the need to use a specific prior distribution. The loss functions considered come naturally from the quadratic error loss function commonly used in estimating a real function of the unknown parameter. The cornerstone of these Bayes estimators is the posterior predictive distribution. Some examples are provided to illustrate the results.

Keywords: Bayesian estimation of a regression curve; posterior predictive distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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