  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. Namely, we are interested in
estimating a regression curve. Simultaneously, the estimation problems of a
conditional distribution function, or a conditional density, or even the
conditional distribution itself, are considered. All these problems are posed
in a sufficiently general framework to cover continuous and discrete,
univariate and multivariate, parametric and non-parametric cases, without the
need to use a specific prior distribution. The loss functions considered come
naturally from the quadratic error loss function comonly used in estimating a
real function of the unknown parameter. The cornerstone of the mentioned Bayes
estimators is the posterior predictive distribution. Some examples are provided
to illustrate these results.
