2015/09/09 by Oleg Chernoyarov, Chernoyarov, Oleg, Yury Kutoyants +3
Mathematics · #62G10 #62G20 #62M02 #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #msc:62G10 #msc:62G20 #msc:62M02 #stat.TH
paper · pdf · doi:10.48550/arxiv.1509.02715
26 pages
arxiv created 2015/09/09 · arxiv updated 2015/09/10
The problem of parameter estimation by the continuous time observations of a deterministic signal in white gaussian noise is considered. The asymptotic properties of the maximul likelihood estimator are described in the asymptotics of small noise (large siglal-to-noise ratio). We are interested by the situation when there is a misspecification in the regularity conditions. In particular it is supposed that the statistician uses a discontinuous (change-point type) model of signal, when the true signal is continuously differentiable function of the unknown parameter.