2015/09/09 by Oleg Chernoyarov, Chernoyarov, Oleg, Serguei Dachian +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.1509.02880
22 pages
arxiv created 2015/09/09 · arxiv updated 2015/09/10
We consider the problem of parameter estimation by the observations of deterministic signal in white gaussian noise. It is supposed that the signal has a singularity of cusp-type. The properties of the maximum likelihood and bayesian estimators are described in the asymptotics of small noise. Special attention is paid to the problem of parameter estimation in the situation of misspecification in regularity, i.e.; the statistician supposes that the observed signal has this singularity, but the real signal is smooth. The rate and the asymptotic distribution of the maximum likelihood estimator in this situation are described.