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Truncated sequential estimation of the parameter of a first order autoregressive process with dependent noises

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Abstract

For a first-order non-explosive autoregressive process with dependent noise, we propose a truncated sequential procedure with a fixed mean-square accuracy. The asymptotic distribution of the estimator depends on the type of the noise distribution: it is normal when the noise has a Kotz’s distribution, while it is a mixture of normal distributions if the noise distribution is a variance mixture of normal distrbutions as well. In both cases, the convergence to the limiting distribution is uniform in the unknown parameter.

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References

  1. J. O. Berger, “Minimax Estimation of Location Vectors for a Wide Class of Densities”, Ann. Statist. 3, 1318–1328 (1975).

    Article  MATH  MathSciNet  Google Scholar 

  2. V. Z. Borisov and V. V. Konev, “Sequential Estimation of Parameters of Discrete Processes,” Automat. and Remote Control 10, 58–64 (1977).

    Google Scholar 

  3. K.-T. Fang, S. Kotz, and K.-W. Ng, Symmetric Multivariate and Related Distributions (Chapman and Hall, 1989).

  4. T. Kariya and B. K. Sinha, The Robustness of Statistical Tests (Academic Press, New York, 1993).

    Google Scholar 

  5. V. V. Konev and S. M. Pergamenshchikov, “Sequential Identification Procedures for the Parameters of Dynamic Systems”, Automat. and Remote Control 7, 84–92 (1981).

    MathSciNet  Google Scholar 

  6. S. Kotz, “Multivariate Distributions at a Cross-Road”, Statistical Distributions in Scientific Work, Ed. by S. Kotz, J. K. Ord, and G. J. Patil (1975), Vol. 1, pp. 245–270.

  7. T. L. Lai and D. Y. Sigmund, “Fixed Accuracy Estimation of an Autoregressive Parameter”, Ann. Statist. 11, 478–485 (1983).

    Article  MATH  MathSciNet  Google Scholar 

  8. N. Mukhopadhyay and T. N. Sriram, “On Sequential Comparisons of Means of First Order Autoregressive Models”, Metrika 39, 155–164 (1992).

    Article  MATH  MathSciNet  Google Scholar 

  9. T. N. Sriram, “Sequential Estimation of the Mean of a First Order Stationary Autoregressive Process”, Ann. Statist. 15, 1079–1090 (1987).

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. LITIS EA 4108, Univ. Rouen, Rouen, France

    D. Fourdrinier

  2. Dept. Appl. Math. and Cybernetics, Tomsk State University, Tomsk, Russia

    V. Konev

  3. Laboratoire de Math. R. Salem, Univ. Rouen, Rouen, France

    S. Pergamenshchikov

Authors
  1. D. Fourdrinier
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  2. V. Konev
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  3. S. Pergamenshchikov
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Correspondence to D. Fourdrinier.

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Fourdrinier, D., Konev, V. & Pergamenshchikov, S. Truncated sequential estimation of the parameter of a first order autoregressive process with dependent noises. Math. Meth. Stat. 18, 43–58 (2009). https://doi.org/10.3103/S1066530709010037

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  • DOI: https://doi.org/10.3103/S1066530709010037

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