2009/05/10 by Yannick Baraud, Baraud, Yannick · 1 citation
Mathematics · #62G05 #Advanced Statistical Methods and Models #FOS: Mathematics #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #msc:62G05 #stat.TH
paper · pdf · doi:10.48550/arxiv.0905.1486
arxiv created 2009/05/10 · openalex publication_date 2009/05/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We observe a random measure N and aim at estimating its intensity s. This statistical framework allows to deal simultaneously with the problems of estimating a density, the marginals of a multivariate distribution, the mean of a random vector with nonnegative components and the intensity of a Poisson process. Our estimation strategy is based on estimator selection. Given a family of estimators of s based on the observation of N, we propose a selection rule, based on N as well, in view of selecting among these. Little assumption is made on the collection of estimators. The procedure offers the possibility to perform model selection and also to select among estimators associated to different model selection strategies. Besides, it provides an alternative to the T-estimators as studied recently in Birgé (2006). For illustration, we consider the problems of estimation and (complete) variable selection in various regression settings.