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Asymptotic normality of the maximum likelihood estimate in the independent not identically distributed case

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Abstract

In this paper, we assume the existence and consistency of the maximum likelihood estimate (MLE) in the independent not identically distributed (i.n.i.d.) case and we establish its asymptotic normality. The regularity conditions employed do not involve the third order derivatives of the underlying probability density functions (p.d.f.'s).

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Author information

Authors and Affiliations

  1. University of Texas, Texas, USA

    A. N. Philippou & G. G. Roussas

  2. University of Wisconsin, Wisconsin, USA

    A. N. Philippou & G. G. Roussas

  3. University of Patras, Patras, Greece

    A. N. Philippou & G. G. Roussas

Authors
  1. A. N. Philippou
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  2. G. G. Roussas
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Additional information

This research was supported by the National Science Foundation, Grant GR-20036, and the Office of Scientific Research and Development of the Greek Government.

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Philippou, A.N., Roussas, G.G. Asymptotic normality of the maximum likelihood estimate in the independent not identically distributed case. Ann Inst Stat Math 27, 45–55 (1975). https://doi.org/10.1007/BF02504623

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  • DOI: https://doi.org/10.1007/BF02504623

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