Abstract
Under some regularity conditions, it is well known that the maximum likelihood estimator (MLE) is asymptotically normal and efficient. However, if the observation is contaminated, the MLE is not always an appropriate estimator. In this paper, we treat M-estimators and study their asymptotic behavior. By choosing estimation equations, robust M-estimators are presented for phase parameters.
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References
Bustos, O. and Yohai, V. J. (1986). Robust estimators for ARMA models. J. Amer. Statist. Assoc., 81, 155–168.
Denby, I. and Martin, R. D. (1979). Robust estimation of the first order autoregressive parameter. J. Amer. Statist. Assoc., 74, 140–146.
Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J. and Stahel, W. A. (1986). Robust Statistics. Wiley, New York.
Huber, P. J. (1981). Robust Statistics. Wiley, New York.
Kleiner, B., Martin, R. D. and Thomson, D. J. (1979). Robust estimation of power spectra, J. Roy. Statist. Soc. Ser. B. 41, 313–351.
Künsch, H. (1984). Infinitesimal robustness for autoregressive processes. Ann. Statist., 12, 843–863.
Kutoyants, Yu. A. (1984). Parameter Estimation for Stochastic Processes, (translated by B. S. L. Prakasa Rao), Heldermann Verlag, Berlin.
Martin, R. D. and Yohai, V. J. (1985). Robustness in time series and estimating ARMA models. Handbook of Statistics, Vol. 5, 119–155, North-Holland, Amsterdam.
Martin, R. D. and Yohai, V. J. (1986). Influence functionals for time series. Ann. Statist., 14, 781–818.
Yoshida, N. (1988). Robust M-estimator in diffusion processes. Ann. Inst. Statist. Math., 40, 799–820.
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Yoshida, N., Hayashi, T. On the robust estimation in poisson processes with periodic intensities. Ann Inst Stat Math 42, 489–507 (1990). https://doi.org/10.1007/BF00049304
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DOI: https://doi.org/10.1007/BF00049304