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Least Absolute Deviation Estimation for Regression with ARMA Errors

Author

Listed:
  • Richard A. Davis

    (Colorado State University)

  • William T. M. Dunsmuir

    (University of New South Wales)

Abstract

The asymptotic normality for least absolute deviation estimates of the parameters in a linear regression model with autoregressive moving average errors is established under very general conditions. The method of proof is based on a functional limit theorem for the LAD objective function.

Suggested Citation

  • Richard A. Davis & William T. M. Dunsmuir, 1997. "Least Absolute Deviation Estimation for Regression with ARMA Errors," Journal of Theoretical Probability, Springer, vol. 10(2), pages 481-497, April.
    • Handle: RePEc:spr:jotpro:v:10:y:1997:i:2:d:10.1023_a:1022620818679
    DOI: 10.1023/A:1022620818679
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    References listed on IDEAS

    as
    1. William T. M. Dunsmuir & Nancy M. Spencer, 1991. "Strong Consistency And Asymptotic Normality Of /1 Estimates Of The Autoregressive Moving‐Average Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 12(2), pages 95-104, March.
    2. Davis, Richard A. & Knight, Keith & Liu, Jian, 1992. "M-estimation for autoregressions with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 145-180, February.
    3. Davis, Richard A. & Dunsmuir, William T.M., 1996. "Maximum Likelihood Estimation for MA(1) Processes with a Root on or near the Unit Circle," Econometric Theory, Cambridge University Press, vol. 12(1), pages 1-29, March.
    4. Davis, Richard A., 1996. "Gauss-Newton and M-estimation for ARMA processes with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 63(1), pages 75-95, October.
    5. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Bardet, Jean-Marc, 2023. "Laplace’s method and BIC model selection for least absolute value criterion," Statistics & Probability Letters, Elsevier, vol. 195(C).

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