On two estimates related to the change-point problem

2011/12/16 by Farida Enikeeva, Enikeeva, Farida
Computer Science · Decision Sciences · Mathematics · #Advanced Statistical Process Monitoring #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1112.3729

arxiv created 2011/12/16 · openalex publication_date 2011/12/16 · arxiv updated 2011/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the problem of estimating a smooth functional of an unknown signal with discontinuity from Gaussian observations. The signal is a known function that depends on an unknown parameter. This problem is closely related to the famous change-point problem. We obtain an asymptotic likelihood ratio process for the noise level tending to 0. Bayesian and maximum likelihood estimates are constructed and their relative efficiency is studied. Some simulation results and conclusions on non-asymptotic behavior of these estimates are presented.

Citations

• A Shift Of The Mean Level In A Sequence Of Independent Normal Random Variables—A Bayesian Approach—

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