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Conditional maximum Lq-likelihood estimation for regression model with autoregressive error terms

Author

Listed:
  • Yeşim Güney

    (Ankara University)

  • Y. Tuaç

    (Ankara University)

  • Ş. Özdemir

    (Afyon Kocatepe University)

  • O. Arslan

    (Ankara University)

Abstract

In this article, we consider the parameter estimation of regression model with pth-order autoregressive (AR(p)) error term. We use the maximum Lq-likelihood (MLq) estimation method proposed by Ferrari and Yang (Ann Stat 38(2):753–783, 2010), as a robust alternative to the classical maximum likelihood (ML) estimation method to handle the outliers in the data. After exploring the MLq estimators for the parameters of interest, we provide some asymptotic properties of the resulting MLq estimators. We give a simulation study and three real data examples to illustrate the performance of the proposed estimators over the ML estimators and observe that the MLq estimators have superiority over the ML estimators when some outliers are present in the data.

Suggested Citation

  • Yeşim Güney & Y. Tuaç & Ş. Özdemir & O. Arslan, 2021. "Conditional maximum Lq-likelihood estimation for regression model with autoregressive error terms," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(1), pages 47-74, January.
    • Handle: RePEc:spr:metrik:v:84:y:2021:i:1:d:10.1007_s00184-020-00774-2
    DOI: 10.1007/s00184-020-00774-2
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    References listed on IDEAS

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    1. Chao Huang & Jin-Guan Lin & Yan-Yan Ren, 2013. "Testing for the shape parameter of generalized extreme value distribution based on the $$L_q$$ -likelihood ratio statistic," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(5), pages 641-671, July.
    2. Davide Ferrari & Sandra Paterlini, 2009. "The Maximum Lq-Likelihood Method: An Application to Extreme Quantile Estimation in Finance," Methodology and Computing in Applied Probability, Springer, vol. 11(1), pages 3-19, March.
    3. Beach, Charles M & MacKinnon, James G, 1978. "A Maximum Likelihood Procedure for Regression with Autocorrelated Errors," Econometrica, Econometric Society, vol. 46(1), pages 51-58, January.
    4. Davide Ferrari & Sandra Paterlini, 2010. "Efficient and robust estimation for financial returns: an approach based on q-entropy," Department of Economics 0623, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
    5. Ronchetti, Elvezio, 1985. "Robust model selection in regression," Statistics & Probability Letters, Elsevier, vol. 3(1), pages 21-23, February.
    6. Fatma Zehra Doğru & Y. Murat Bulut & Olcay Arslan, 2018. "Doubly reweighted estimators for the parameters of the multivariate t-distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(19), pages 4751-4771, October.
    7. Yichen Qin & Carey E. Priebe, 2013. "Maximum L q -Likelihood Estimation via the Expectation-Maximization Algorithm: A Robust Estimation of Mixture Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 914-928, September.
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