2012/10/23 by B. J. K. Kleijn, Bas Kleijn, Kleijn, Bas +2 · 1 citation
Computer Science · Mathematics · #62F15 (Secondary) #62G20 (Primary) 62G15 #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #msc:62F15 #msc:62G15 #msc:62G20 #stat.TH
paper · pdf · doi:10.48550/arxiv.1210.6204
openalex publication_date 2012/10/23 · arxiv created 2013/12/18 · arxiv updated 2013/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider semiparametric models that display local asymptotic exponentiality (Ibragimov and Has'minskii (1981)), an asymptotic property of the likelihood associated with discontinuities of densities. Our interest goes to estimation of the location of such discontinuities while other aspects of the density form a nuisance parameter. It is shown that under certain conditions on model and prior, the posterior distribution displays Bernstein-von Mises-type asymptotic behaviour, with exponential distributions as the limiting sequence. In contrast to regular settings, the maximum likelihood estimator is inefficient under this form of irregularity. However, Bayesian point estimators based on the limiting posterior distribution attain the minimax risk. Therefore, the limiting behaviour of the posterior is used to advocate efficiency of Bayesian point estimation rather than compare it to frequentist estimation procedures based on the maximum likelihood estimator. Results are applied to semiparametric LAE location and scaling examples.