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Conditions equivalent to consistency of approximate MLE's for stochastic processes

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  • Vajda, Igor

Abstract

Maximum likelihood and approximate maximum likelihood estimates of parameters of random processes are considered. A mild regularity is assumed under which these estimates exist. Conditions necessary and sufficient for consistency of all approximate maximum likelihood estimates are established. These conditions are first applied to i.i.d. observations and the result is shown to be in some sense sharper than what is known from the literature. Then new consistency results are obtained by applying these conditions to observations from various concrete classes of discrete and continuous processes.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:56:y:1995:i:1:p:35-56
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    References listed on IDEAS

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    1. Luschgy, Harald & Rukhin, Andrew L. & Vajda, Igor, 1993. "Adaptive tests for stochastic processes in the ergodic case," Stochastic Processes and their Applications, Elsevier, vol. 45(1), pages 45-59, March.
    2. J. Pfanzagl, 1969. "On the measurability and consistency of minimum contrast estimates," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 14(1), pages 249-272, December.
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    Cited by:

    1. A. Mayoral & D. Morales & J. Morales & I. Vajda, 2003. "On efficiency of estimation and testing with data quantized to fixed number of cells," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 57(1), pages 1-27, February.
    2. 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.

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