On misspecifications in regularity and properties of estimators O. V. Chernoyarov, Y. A. Kutoyants, A. P. Trifonov
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ArticleSubject(s): белый гауссовский шум | асимптотические свойства оценки максимального правдоподобияGenre/Form: статьи в журналах Online resources: Click here to access online
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Electronic journal of statistics Vol. 12, № 1. P. 80-106Abstract: 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 maximum likelihood estimator are described in the asymptotic of small noise (large signal-to-noise ratio). We are interested in 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.
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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 maximum likelihood estimator are described in the asymptotic of small noise (large signal-to-noise ratio). We are interested in 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.
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