On a class of M-estimators for Gaussian long-memory models

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1994
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Zusammenfassung

We consider estimation for parametric stationary Gaussian models with long memory. The spectral density f(x; θ) is assumed to be characterised by a vector θ = (θ1, θ2, θ3,…, θm) such that θ2 = H ε (½, 1) and f(x; θ) is proportional to x1−2H as x tends to zero. An approximate maximum likelihood estimator based on the autoregressive representation of the process is proposed. Its asymptotic distribution is derived. More generally, the approach leads to a class of M-estimators for which a central limit theorem holds. By choosing an appropriate ψ-function, robustness against additive outliers can be achieved, while keeping high efficiency under the ideal model. This is illustrated by a small simulation study. A simple algorithm and an explicit formula for the efficiency, and thus for choosing an appropriate tuning parameter, are given for Hampel's redescending ψ-function.

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Fachgebiet (DDC)
510 Mathematik
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Autoregressive, Fractional ARIMA, Influence function, Long-range dependence, Maximum likelihood estimation, Redescending function, Robustness
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ISO 690BERAN, Jan, 1994. On a class of M-estimators for Gaussian long-memory models. In: Biometrika. 1994, 81(4), pp. 755-766. ISSN 0006-3444. Available under: doi: 10.1093/biomet/81.4.755
BibTex
@article{Beran1994class-18822,
  year={1994},
  doi={10.1093/biomet/81.4.755},
  title={On a class of M-estimators for Gaussian long-memory models},
  number={4},
  volume={81},
  issn={0006-3444},
  journal={Biometrika},
  pages={755--766},
  author={Beran, Jan}
}
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