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On asymptotically optimal estimates for general observations

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  • Vajda, Igor
  • Janzura, Martin

Abstract

Asymptotically maximum likelihood estimators and estimators asymptotically minimizing criterial functions of observations are considered in statistical models with generalized sequences of observations. New necessary and sufficient conditions for consistency of these estimators are established. The applicability of these conditions is illustrated on regression models with Gaussian and contaminated observations and on models of exponentially distributed random processes and fields.

Suggested Citation

  • Vajda, Igor & Janzura, Martin, 1997. "On asymptotically optimal estimates for general observations," Stochastic Processes and their Applications, Elsevier, vol. 72(1), pages 27-45, December.
    • Handle: RePEc:eee:spapps:v:72:y:1997:i:1:p:27-45
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    References listed on IDEAS

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    1. Vajda, Igor, 1995. "Conditions equivalent to consistency of approximate MLE's for stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 56(1), pages 35-56, March.
    2. Luschgy Harald, 1993. "Second Order Behavior Of Neyman-Pearson Tests For Stochastic Processes," Statistics & Risk Modeling, De Gruyter, vol. 11(2), pages 133-150, February.
    3. DRYGAS, Hilmar, 1976. "Weak and strong consistency of the least squares estimators in regression models," LIDAM Reprints CORE 236, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Liese, F. & Vajda, I., 1994. "Consistency of M-Estimates in General Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 93-114, July.
    5. Friedrich Liese & Igor Vajda, 1995. "Necessary and sufficient conditions for consistency of generalizedM-estimates," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 42(1), pages 291-324, December.
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