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R-estimation in Autoregression with Square-Integrable Score Function

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  • Mukherjee, Kanchan
  • Bai, Z. D.

Abstract

This paper develops an asymptotic theory for R-estimation based on a square-integrable, not necessarily bounded, score function in the pth order stationary autoregressive model. Asymptotic uniform linearity of a class of linear rank statistics is established and the asymptotic normality of the corresponding R-estimators is derived. This paper thus solves a long-standing problem in the development of the asymptotics for rank estimators under the autoregressive setup. The proofs use a combination of the approximation technique, the contiguity technique and the weak convergence technique of Hajek, Jurecková and Koul, respectively.

Suggested Citation

  • Mukherjee, Kanchan & Bai, Z. D., 2002. "R-estimation in Autoregression with Square-Integrable Score Function," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 167-186, April.
    • Handle: RePEc:eee:jmvana:v:81:y:2002:i:1:p:167-186
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    References listed on IDEAS

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    1. Marc Hallin & Madan Lal Puri, 1994. "Aligned rank tests for linear models with autocorrelated errors," ULB Institutional Repository 2013/2045, ULB -- Universite Libre de Bruxelles.
    2. Marc Hallin & Jean-François Ingenbleek & Madan Lal Puri, 1984. "Linear serial rank tests for randomness against ARMA alternatives," ULB Institutional Repository 2013/2167, ULB -- Universite Libre de Bruxelles.
    3. Hallin, M. & Puri, M. L., 1994. "Aligned Rank Tests for Linear Models with Autocorrelated Error Terms," Journal of Multivariate Analysis, Elsevier, vol. 50(2), pages 175-237, August.
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    Cited by:

    1. M. Hallin & D. La Vecchia & H. Liu, 2022. "Center-Outward R-Estimation for Semiparametric VARMA Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(538), pages 925-938, April.
    2. Hallin, Marc & La Vecchia, Davide, 2020. "A Simple R-estimation method for semiparametric duration models," Journal of Econometrics, Elsevier, vol. 218(2), pages 736-749.
    3. Mukherjee, Kanchan, 2007. "Generalized R-estimators under conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 141(2), pages 383-415, December.
    4. Marc Hallin & Davide La Vecchia, 2014. "Semiparametrically Efficient R-Estimation for Dynamic Location-Scale Models," Working Papers ECARES ECARES 2014-45, ULB -- Universite Libre de Bruxelles.
    5. Hallin, Marc & La Vecchia, Davide, 2017. "R-estimation in semiparametric dynamic location-scale models," Journal of Econometrics, Elsevier, vol. 196(2), pages 233-247.
    6. Hang Liu & Kanchan Mukherjee, 2022. "R-estimators in GARCH models: asymptotics and applications [Rank-based estimation for GARCH processes]," The Econometrics Journal, Royal Economic Society, vol. 25(1), pages 98-113.

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