2021/10/26 by A. G. Nogales, Nogales, A. G.
Decision Sciences · Mathematics · #62G07 Secondary: 62Jxx #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #FOS: Mathematics #Primary: 62F15 #Statistical Methods and Bayesian Inference #Statistics Theory (math.ST) #math.ST #msc:62F15 #msc:62G07 #msc:62Jxx #stat.TH
paper · pdf · doi:10.48550/arxiv.2110.13427
16 pages
arxiv created 2021/10/26 · openalex publication_date 2021/10/26 · arxiv updated 2021/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.