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On efficiency of estimation and testing with data quantized to fixed number of cells

Author

Listed:
  • A. Mayoral
  • D. Morales
  • J. Morales
  • I. Vajda

Abstract

In continuous parametrized models with i.i.d. observations we consider finite quantizations. We study asymptotic properties of the estimators minimizing disparity between the observed and expected frequencies in the quantization cells, and asymptotic properties of the goodness of fit tests rejecting the hypotheses when the disparity is large. The disparity is measured by an appropriately generalized φ-divergence of probability distributions so that, by the choice of function φ, one can control the properties of estimators and tests. For bounded functions φ these procedures are robust. We show that the inefficiency of the estimators and tests can be measured by the decrease of the Fisher information due to the quantization. We investigate theoretically and numerically the convergence of the Fisher informations. The results indicate that, in the common families, the quantizations into 10–20 cells guarantees “practical efficiency” of the quantization-based procedures. These procedures can at the same time be robust and numerically considerably simpler than similar procedures using the unreduced data. Copyright Springer-Verlag 2003

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:57:y:2003:i:1:p:1-27
    DOI: 10.1007/s001840100178
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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.
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    Cited by:

    1. M. Ekström & S. M. Mirakhmedov & S. Rao Jammalamadaka, 2020. "A class of asymptotically efficient estimators based on sample spacings," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 617-636, September.

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